Pub Date : 2025-11-08DOI: 10.1016/j.nonrwa.2025.104529
Ming Lu, Chenxi Su
In this paper, we study compressible Navier-Stokes systems for non-isentropic fluids subject to rotational effects under strong gravitational stratification, focusing on the multi-scale asymptotic analysis of the problem. Key dimensionless parameters-including the Mach number, Froude number, Péclet number, and Rossby number-are scaled with specific powers of the small parameter . In particular, the Mach number and the Froude number are assumed to be of the same order in . Moreover, the Reynolds number is considered to approach infinity as . Our analysis shows that the limiting system corresponds to a variant of the two-dimensional incompressible Euler equations.
{"title":"Non-isentropic rotating compressible fluids under strong stratification","authors":"Ming Lu, Chenxi Su","doi":"10.1016/j.nonrwa.2025.104529","DOIUrl":"10.1016/j.nonrwa.2025.104529","url":null,"abstract":"<div><div>In this paper, we study compressible Navier-Stokes systems for non-isentropic fluids subject to rotational effects under strong gravitational stratification, focusing on the multi-scale asymptotic analysis of the problem. Key dimensionless parameters-including the Mach number, Froude number, Péclet number, and Rossby number-are scaled with specific powers of the small parameter <span><math><mi>ϵ</mi></math></span>. In particular, the Mach number and the Froude number are assumed to be of the same order in <span><math><mi>ϵ</mi></math></span>. Moreover, the Reynolds number is considered to approach infinity as <span><math><mrow><mi>ϵ</mi><mo>→</mo><mn>0</mn></mrow></math></span>. Our analysis shows that the limiting system corresponds to a variant of the two-dimensional incompressible Euler equations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104529"},"PeriodicalIF":1.8,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-07DOI: 10.1016/j.nonrwa.2025.104534
Jacopo Borsotti , Mattia Sensi
We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models.
{"title":"A geometric analysis of the Bazykin-Berezovskaya predator-prey model with Allee effect in an economic framework","authors":"Jacopo Borsotti , Mattia Sensi","doi":"10.1016/j.nonrwa.2025.104534","DOIUrl":"10.1016/j.nonrwa.2025.104534","url":null,"abstract":"<div><div>We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form. We completely characterize its dynamics, providing explicit threshold quantities to distinguish between a rich variety of possible asymptotic behaviors. Moreover, we propose numerical results to illustrate our findings. Lastly, we comment on the real-world interpretation of these results, in an economic framework and in the context of predator-prey models.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104534"},"PeriodicalIF":1.8,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-06DOI: 10.1016/j.nonrwa.2025.104535
Wenwen Huo , Chao Zhang
This paper concerns the global existence and optimal time-decay rate for the higher-order spatial derivative of classical solutions for the three-dimensional viscous and heat-conductive fluids, which is governed by the compressible Navier-Stokes (CNS) system with an external potential force. We first establish the global existence of the non-isentropic CNS system with potential force when the initial data is a small perturbation near the equilibrium state. Subsequently, we show the upper and lower bounds of the optimal decay rates for the solution and its spatial derivatives based on energy estimate and low-high frequency decomposition.
{"title":"Global existence and optimal time-decay rates of 3D non-isentropic compressible Navier-Stokes system with potential force","authors":"Wenwen Huo , Chao Zhang","doi":"10.1016/j.nonrwa.2025.104535","DOIUrl":"10.1016/j.nonrwa.2025.104535","url":null,"abstract":"<div><div>This paper concerns the global existence and optimal time-decay rate for the higher-order spatial derivative of classical solutions for the three-dimensional viscous and heat-conductive fluids, which is governed by the compressible Navier-Stokes (CNS) system with an external potential force. We first establish the global existence of the non-isentropic CNS system with potential force when the initial data is a small perturbation near the equilibrium state. Subsequently, we show the upper and lower bounds of the optimal decay rates for the solution and its spatial derivatives based on energy estimate and low-high frequency decomposition.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104535"},"PeriodicalIF":1.8,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-05DOI: 10.1016/j.nonrwa.2025.104528
Hong-Jie Wu, Bang-Sheng Han, Hong-Lei Wei, Yinghui Yang
The study investigates pulsating wave speeds in an advective two-species competition-diffusion system under periodic environments. Recent studies have confirmed the existence and characterized the qualitative dynamics of pulsating waves. In this paper, we determine pulsating wave speed’s signs with identical diffusion rates and characterize invasion dynamics of competing species in heterogeneous environments by comparing the reactions and competitions. Specifically, we first establish a criterion for zero-speed waves and derive sufficient conditions for strictly positive or negative speeds. Our framework extends previous studies (e.g., Ding and Liang, Math. Ann. 385 (2023), 1–36) by considering functional representation of periodic steady-state solutions and explicit inclusion of advection effects and extends (e.g., Du et al., Z. Angew. Math. Phys. 71 (2020), 27 pp.) by further considering the sign of the pulsating wave speed, determining the long-time behavior of two strongly competing species. Crucially, the presence of the advection term indeed exerts a certain influence on the long-time behavior of two strongly competing species: From the perspective of the proof process, the appearance of the advection term increased the difficulty and complexity of proving Lemmas 2.3 and 3.1; from the result perspective, the advection term necessitates specific structural conditions for definitive speed determination. These findings advance understanding of pattern selection mechanisms in flow-driven ecological systems.
{"title":"Spreading speeds for a Lotva-Volterra competition system with advection in a periodic habitat","authors":"Hong-Jie Wu, Bang-Sheng Han, Hong-Lei Wei, Yinghui Yang","doi":"10.1016/j.nonrwa.2025.104528","DOIUrl":"10.1016/j.nonrwa.2025.104528","url":null,"abstract":"<div><div>The study investigates pulsating wave speeds in an advective two-species competition-diffusion system under periodic environments. Recent studies have confirmed the existence and characterized the qualitative dynamics of pulsating waves. In this paper, we determine pulsating wave speed’s signs with identical diffusion rates and characterize invasion dynamics of competing species in heterogeneous environments by comparing the reactions and competitions. Specifically, we first establish a criterion for zero-speed waves and derive sufficient conditions for strictly positive or negative speeds. Our framework extends previous studies (e.g., Ding and Liang, Math. Ann. 385 (2023), 1–36) by considering functional representation of periodic steady-state solutions and explicit inclusion of advection effects and extends (e.g., Du et al., Z. Angew. Math. Phys. 71 (2020), 27 pp.) by further considering the sign of the pulsating wave speed, determining the long-time behavior of two strongly competing species. Crucially, the presence of the advection term indeed exerts a certain influence on the long-time behavior of two strongly competing species: From the perspective of the proof process, the appearance of the advection term increased the difficulty and complexity of proving Lemmas 2.3 and 3.1; from the result perspective, the advection term necessitates specific structural conditions for definitive speed determination. These findings advance understanding of pattern selection mechanisms in flow-driven ecological systems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104528"},"PeriodicalIF":1.8,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-02DOI: 10.1016/j.nonrwa.2025.104530
Douglas R. Anderson , Masakazu Onitsuka
The Hyers–Ulam stability of a first-order nonlinear differential equation based on a generalized Richards growth model (also known as a Savageau growth model) is conditionally established based on the maximum size of the perturbation being not too large and the initial condition being not too small in terms of the carrying capacity and the powers involved. The Hyers–Ulam stability constants are determined explicitly and are shown to depend on the relative sizes of the power parameters in the model. Examples are provided of both stability and instability to illustrate the sharpness of our results. The main result is then applied to a tissue growth model. These results generalize known stability properties of the logistic equation and contribute to the theory of functional stability in nonlinear differential equations, with implications for population and biological models and related applications.
{"title":"A generalized Richards growth model with conditional Hyers-Ulam stability","authors":"Douglas R. Anderson , Masakazu Onitsuka","doi":"10.1016/j.nonrwa.2025.104530","DOIUrl":"10.1016/j.nonrwa.2025.104530","url":null,"abstract":"<div><div>The Hyers–Ulam stability of a first-order nonlinear differential equation based on a generalized Richards growth model (also known as a Savageau growth model) is conditionally established based on the maximum size of the perturbation being not too large and the initial condition being not too small in terms of the carrying capacity and the powers involved. The Hyers–Ulam stability constants are determined explicitly and are shown to depend on the relative sizes of the power parameters in the model. Examples are provided of both stability and instability to illustrate the sharpness of our results. The main result is then applied to a tissue growth model. These results generalize known stability properties of the logistic equation and contribute to the theory of functional stability in nonlinear differential equations, with implications for population and biological models and related applications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104530"},"PeriodicalIF":1.8,"publicationDate":"2025-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-11-01DOI: 10.1016/j.nonrwa.2025.104525
Yuting Xiang
<div><div>The two-species doubly degenerate nutrient taxis model with competitive kinetics<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><mrow></mrow><msub><mi>u</mi><mrow><mn>1</mn><mi>t</mi></mrow></msub></mrow></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>1</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>1</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>1</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>u</mi><mrow><mn>2</mn><mi>t</mi></mrow></msub></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>2</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>2</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>2</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>2</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>2</mn></msub><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>v</mi><mi>t</mi></msub></mtd><mtd><mrow><mo>=</mo><msub><mi>v</mi><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>−</mo><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>is considered under no-flux boundary conditions in an open bounded interval <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi></mrow></math></span>, where <span><math><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mi>μ</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> for <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>. It is shown that for all suitably regular nonnegative initial data <span><math><mrow><mo>(</mo><msub><mi>u</mi><mn>10</mn></msub><mo>,</mo><msub><mi>u</mi><mn>20</mn></msub><mo>,</mo><msub><mi>v</mi><mn>0</mn></msub><mo>)</mo></mrow></math></span>, where <span><math><ms
{"title":"Boundedness and large-time behavior in a two-species doubly degenerate diffusion chemotaxis system with logistic proliferation","authors":"Yuting Xiang","doi":"10.1016/j.nonrwa.2025.104525","DOIUrl":"10.1016/j.nonrwa.2025.104525","url":null,"abstract":"<div><div>The two-species doubly degenerate nutrient taxis model with competitive kinetics<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><mrow></mrow><msub><mi>u</mi><mrow><mn>1</mn><mi>t</mi></mrow></msub></mrow></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>1</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>1</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>1</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>1</mn></msub><mo>−</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>u</mi><mrow><mn>2</mn><mi>t</mi></mrow></msub></mtd><mtd><mrow><mo>=</mo><msub><mrow><mo>(</mo><msub><mi>u</mi><mn>2</mn></msub><mi>v</mi><msub><mi>u</mi><mrow><mn>2</mn><mi>x</mi></mrow></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>−</mo><msub><mrow><mo>(</mo><msubsup><mi>u</mi><mn>2</mn><mn>2</mn></msubsup><mi>v</mi><msub><mi>v</mi><mi>x</mi></msub><mo>)</mo></mrow><mi>x</mi></msub><mo>+</mo><msub><mi>μ</mi><mn>2</mn></msub><msub><mi>u</mi><mn>2</mn></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mi>u</mi><mn>2</mn></msub><mo>−</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>u</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr><mtr><mtd><msub><mi>v</mi><mi>t</mi></msub></mtd><mtd><mrow><mo>=</mo><msub><mi>v</mi><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>−</mo><mrow><mo>(</mo><msub><mi>u</mi><mn>1</mn></msub><mo>+</mo><msub><mi>u</mi><mn>2</mn></msub><mo>)</mo></mrow><mi>v</mi><mo>,</mo></mrow></mtd><mtd><mrow><mi>x</mi><mo>∈</mo><mstyle><mi>Ω</mi></mstyle><mo>,</mo><mi>t</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>is considered under no-flux boundary conditions in an open bounded interval <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi></mrow></math></span>, where <span><math><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mi>μ</mi><mi>i</mi></msub><mo>></mo><mn>0</mn></mrow></math></span> for <span><math><mrow><mo>(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>. It is shown that for all suitably regular nonnegative initial data <span><math><mrow><mo>(</mo><msub><mi>u</mi><mn>10</mn></msub><mo>,</mo><msub><mi>u</mi><mn>20</mn></msub><mo>,</mo><msub><mi>v</mi><mn>0</mn></msub><mo>)</mo></mrow></math></span>, where <span><math><ms","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104525"},"PeriodicalIF":1.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145418267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-29DOI: 10.1016/j.nonrwa.2025.104527
Thi Ngoc Ha Vu, Thieu Huy Nguyen
We study the Navier-Stokes equations in a rotating framework near the surface Ekman layer and establish the existence and polynomial stability of a time-periodic solution under the action of a time-periodic external force. Furthermore, when the external forcing is almost periodic in time, we prove the existence and stability of an almost periodic solution. These results describe the nonlinear dynamics of (almost) harmonic oscillations around the surface Ekman spiral. In the absence of external forcing, the nonlinear stability of the Ekman spiral profile follows as a direct consequence.
{"title":"Harmonic oscillations and their stability around surface Ekman layer","authors":"Thi Ngoc Ha Vu, Thieu Huy Nguyen","doi":"10.1016/j.nonrwa.2025.104527","DOIUrl":"10.1016/j.nonrwa.2025.104527","url":null,"abstract":"<div><div>We study the Navier-Stokes equations in a rotating framework near the surface Ekman layer and establish the existence and polynomial stability of a time-periodic solution under the action of a time-periodic external force. Furthermore, when the external forcing is almost periodic in time, we prove the existence and stability of an almost periodic solution. These results describe the nonlinear dynamics of (almost) harmonic oscillations around the surface Ekman spiral. In the absence of external forcing, the nonlinear stability of the Ekman spiral profile follows as a direct consequence.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104527"},"PeriodicalIF":1.8,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-28DOI: 10.1016/j.nonrwa.2025.104524
Xiaodan Chen, Renhao Cui
In this paper, we are concerned with a diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with saturated incidence mechanism and birth-death effect. The basic reproduction number has been derived through a variational expression and determined the threshold dynamics. We mainly investigate spatial profiles of endemic equilibrium with respect to large advection, small dispersal of susceptible/infected individuals and large saturation. These results may offer some prospective applications on disease control and prediction.
{"title":"Spatial profiles of a diffusion-advection epidemic model with saturated incidence mechanism and birth-death effect","authors":"Xiaodan Chen, Renhao Cui","doi":"10.1016/j.nonrwa.2025.104524","DOIUrl":"10.1016/j.nonrwa.2025.104524","url":null,"abstract":"<div><div>In this paper, we are concerned with a diffusion-advection SIS (susceptible-infected-susceptible) epidemic model with saturated incidence mechanism and birth-death effect. The basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> has been derived through a variational expression and determined the threshold dynamics. We mainly investigate spatial profiles of endemic equilibrium with respect to large advection, small dispersal of susceptible/infected individuals and large saturation. These results may offer some prospective applications on disease control and prediction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104524"},"PeriodicalIF":1.8,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-27DOI: 10.1016/j.nonrwa.2025.104526
Na Li
This paper is devoted to studying propagation dynamics in an age-structured population model incorporating two interacting nonlocal mechanisms. We analyze how interactions between nonlocal dispersal kernels shape propagation dynamics based on comparison arguments and the evolutionary viewpoint. By appealing to monotone dynamical system theory, we investigate the existence of spreading speed and its variational characterization. By developing a framework for establishing the fundamental solution and its refined estimates, we construct sub- and super-solutions to rigorously prove the sharp rate of accelerating propagation, which is closely related to the tail heaviness of the convolution of two nonlocal dispersal kernels. Additionally, the influence of time delay on the rate of propagation is discussed under specific conditions. Our findings reveal the crucial role of interactions between nonlocal dispersal kernels in determining the rate of propagation.
{"title":"Sharp rate of accelerating propagation in a nonlocal model arising in population dynamics","authors":"Na Li","doi":"10.1016/j.nonrwa.2025.104526","DOIUrl":"10.1016/j.nonrwa.2025.104526","url":null,"abstract":"<div><div>This paper is devoted to studying propagation dynamics in an age-structured population model incorporating two interacting nonlocal mechanisms. We analyze how interactions between nonlocal dispersal kernels shape propagation dynamics based on comparison arguments and the evolutionary viewpoint. By appealing to monotone dynamical system theory, we investigate the existence of spreading speed and its variational characterization. By developing a framework for establishing the fundamental solution and its refined estimates, we construct sub- and super-solutions to rigorously prove the sharp rate of accelerating propagation, which is closely related to the tail heaviness of the convolution of two nonlocal dispersal kernels. Additionally, the influence of time delay on the rate of propagation is discussed under specific conditions. Our findings reveal the crucial role of interactions between nonlocal dispersal kernels in determining the rate of propagation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104526"},"PeriodicalIF":1.8,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-26DOI: 10.1016/j.nonrwa.2025.104522
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schrödinger-fifth order Korteweg-de Vries systemTo achieve this, we prove a local well-posedness result in Bourgain spaces of the type , along with a regularity property for the nonlinear part of the IVP solutions. This property enables the construction of initial data that leads to the dispersive blow-up phenomenon.
{"title":"Dispersive blow-up for a coupled Schrödinger-fifth order KdV system","authors":"Eddye Bustamante, José Jiménez Urrea, Jorge Mejía","doi":"10.1016/j.nonrwa.2025.104522","DOIUrl":"10.1016/j.nonrwa.2025.104522","url":null,"abstract":"<div><div>In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schrödinger-fifth order Korteweg-de Vries system<span><span><span><math><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mi>i</mi><msub><mi>u</mi><mi>t</mi></msub><mo>+</mo><msubsup><mi>∂</mi><mi>x</mi><mn>2</mn></msubsup><mspace></mspace><mi>u</mi></mrow></mtd><mtd><mrow><mo>=</mo><mi>α</mi><mi>u</mi><mi>v</mi><mo>+</mo><msup><mrow><mi>γ</mi><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mn>2</mn></msup><mspace></mspace><mi>u</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>∂</mi><mi>t</mi></msub><mi>v</mi><mo>+</mo><msubsup><mi>∂</mi><mi>x</mi><mn>5</mn></msubsup><mi>v</mi><mo>+</mo><msub><mi>∂</mi><mi>x</mi></msub><msup><mi>v</mi><mn>2</mn></msup></mrow></mtd><mtd><mrow><mo>=</mo><mi>ϵ</mi><msub><mi>∂</mi><mi>x</mi></msub><msup><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow><mn>2</mn></msup><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mi>R</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mtd><mtd><mrow><mo>=</mo><msub><mi>u</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>v</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mi>v</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>.</mo></mrow></mtd></mtr></mtable><mo>}</mo></mrow></mtd></mtr></mtable></math></span></span></span>To achieve this, we prove a local well-posedness result in Bourgain spaces of the type <span><math><mrow><msup><mi>X</mi><mrow><mi>s</mi><mo>+</mo><mi>β</mi><mo>,</mo><mi>b</mi></mrow></msup><mo>×</mo><msup><mi>Y</mi><mrow><mi>s</mi><mo>,</mo><mi>b</mi></mrow></msup></mrow></math></span>, along with a regularity property for the nonlinear part of the IVP solutions. This property enables the construction of initial data that leads to the dispersive blow-up phenomenon.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104522"},"PeriodicalIF":1.8,"publicationDate":"2025-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145424893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号