Pub Date : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub Date: 2025-10-10DOI: 10.1016/j.nonrwa.2025.104515
Haochuan Huang , Rui Huang , Gege Liu , Jingxue Yin
This paper is concerned with the existence and asymptotic behavior of solutions for the Lane-Emden heat flow system. Our arguments are based on the upper and lower solutions method, which is different from the semigroup techniques and a fixed point theorem in previous works [3, 11]. It is worthy of mentioning that our results do not impose the integrability restrictions on initial values and thus the decay rate exponents of the initial values can be selected as the rescaling invariance exponents for the Lane-Emden heat flow system.
{"title":"Rescaling invariance exponents for the Lane-Emden heat flow system","authors":"Haochuan Huang , Rui Huang , Gege Liu , Jingxue Yin","doi":"10.1016/j.nonrwa.2025.104515","DOIUrl":"10.1016/j.nonrwa.2025.104515","url":null,"abstract":"<div><div>This paper is concerned with the existence and asymptotic behavior of solutions for the Lane-Emden heat flow system. Our arguments are based on the upper and lower solutions method, which is different from the semigroup techniques and a fixed point theorem in previous works [3, 11]. It is worthy of mentioning that our results do not impose the integrability restrictions on initial values and thus the decay rate exponents of the initial values can be selected as the <em>rescaling invariance exponents</em> for the Lane-Emden heat flow system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104515"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270703","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub Date: 2025-10-04DOI: 10.1016/j.nonrwa.2025.104513
Juan Límaco, João Carlos Barreira, Suerlan Silva, Luis P. Yapu
In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control called leader and two controls called followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we find a leader that solves the null controllability problem. The linearized degenerated system is treated adapting Carleman estimates for degenerated systems from Demarque, Límaco and Viana [31] and the local controllability of the non-linear system is obtained using Liusternik’s inverse function theorem. The nonlocal coefficient originates a multiplicative coupling in the optimality system that gives rise to interesting calculations in the applications of the inverse function theorem.
{"title":"Hierarchical null controllability of a degenerate parabolic equation with nonlocal coefficient","authors":"Juan Límaco, João Carlos Barreira, Suerlan Silva, Luis P. Yapu","doi":"10.1016/j.nonrwa.2025.104513","DOIUrl":"10.1016/j.nonrwa.2025.104513","url":null,"abstract":"<div><div>In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control called <em>leader</em> and two controls called <em>followers</em>. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we find a leader that solves the null controllability problem. The linearized degenerated system is treated adapting Carleman estimates for degenerated systems from Demarque, Límaco and Viana [31] and the local controllability of the non-linear system is obtained using Liusternik’s inverse function theorem. The nonlocal coefficient originates a multiplicative coupling in the optimality system that gives rise to interesting calculations in the applications of the inverse function theorem.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104513"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223607","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 : 2026-06-01Epub 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":"2026-06-01","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 : 2026-06-01Epub Date: 2025-10-07DOI: 10.1016/j.nonrwa.2025.104512
Nebi Yılmaz , Muhteşem Demir , Erhan Pişkin
This study explores a higher-order viscoelastic equation characterized by variable exponents. We demonstrate the local existence of weak solutions by imposing appropriate conditions on these variable exponents. Furthermore, we investigate the phenomenon of finite-time blow-up for solutions that begin with positive initial energy. Finally, we give a 2D numerical example for the blow up.
{"title":"Local existence and blow-up of solutions for the higher-order viscoelastic equation with general source term and variable exponents: Theoretical and numerical results","authors":"Nebi Yılmaz , Muhteşem Demir , Erhan Pişkin","doi":"10.1016/j.nonrwa.2025.104512","DOIUrl":"10.1016/j.nonrwa.2025.104512","url":null,"abstract":"<div><div>This study explores a higher-order viscoelastic equation characterized by variable exponents. We demonstrate the local existence of weak solutions by imposing appropriate conditions on these variable exponents. Furthermore, we investigate the phenomenon of finite-time blow-up for solutions that begin with positive initial energy. Finally, we give a 2D numerical example for the blow up.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104512"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270702","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 : 2026-06-01Epub 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":"2026-06-01","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}
Pub Date : 2026-06-01Epub Date: 2025-10-24DOI: 10.1016/j.nonrwa.2025.104523
Taian Jin, Yuxiang Li
<div><div>We study the Neumann initial-boundary value problem for the following quasilinear chemotaxis system with indirect signal production<span><span><span><span><math><mi>★</mi></math></span></span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>S</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>w</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>w</mi><mi>t</mi></msub><mo>+</mo><mi>w</mi><mo>=</mo><mi>u</mi></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>in <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi><msup><mrow></mrow><mi>n</mi></msup></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. Here <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><msub><mi>⨏</mi><mstyle><mi>Ω</mi></mstyle></msub><mi>w</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>D</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>positive</mtext><mspace></mspace><mtext>on</mtext><mspace></mspace><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>S</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>nonnegative</mtext></mrow></math></span>. We prove the following:<ul><li><span>•</span><span><div>If <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>=</mo><msub><mi>B</mi><mi>R</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> with some <span><math><mrow><mi>R</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≤</mo><msub><mi>k</mi><mn>1</mn></msub><mi>s</mi><msup><mrow></mrow><mi>q</mi></msup></mrow></math></span> and <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≥</mo><msub><mi>k</mi><mn>2</mn></msub><mi>s</mi><msup><mrow></mrow><mi>p</mi></msup></mrow></math></span> for all <span><math><mrow><mi>s</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, where <span><math><mrow><msub><mi>k</mi><mn>1</mn></msub><mo>,</mo><msub><mi>k</mi><mn>2</mn></msub><mo>,</mo><mi>p</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mo>
{"title":"Finite time blow-up in a quasilinear Keller-Segel system with indirect signal production","authors":"Taian Jin, Yuxiang Li","doi":"10.1016/j.nonrwa.2025.104523","DOIUrl":"10.1016/j.nonrwa.2025.104523","url":null,"abstract":"<div><div>We study the Neumann initial-boundary value problem for the following quasilinear chemotaxis system with indirect signal production<span><span><span><span><math><mi>★</mi></math></span></span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>∇</mi><mi>u</mi><mo>)</mo></mrow><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>S</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mi>∇</mi><mi>v</mi><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><mn>0</mn><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>μ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>w</mi><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>w</mi><mi>t</mi></msub><mo>+</mo><mi>w</mi><mo>=</mo><mi>u</mi></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>in <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><mi>R</mi><msup><mrow></mrow><mi>n</mi></msup></mrow></math></span> with <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. Here <span><math><mrow><mi>μ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><msub><mi>⨏</mi><mstyle><mi>Ω</mi></mstyle></msub><mi>w</mi><mrow><mo>(</mo><mo>·</mo><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>D</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>positive</mtext><mspace></mspace><mtext>on</mtext><mspace></mspace><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>S</mi><mo>∈</mo><mi>C</mi><msup><mrow></mrow><mn>2</mn></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow><mspace></mspace><mtext>is</mtext><mspace></mspace><mtext>nonnegative</mtext></mrow></math></span>. We prove the following:<ul><li><span>•</span><span><div>If <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>=</mo><msub><mi>B</mi><mi>R</mi></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math></span> with some <span><math><mrow><mi>R</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>D</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≤</mo><msub><mi>k</mi><mn>1</mn></msub><mi>s</mi><msup><mrow></mrow><mi>q</mi></msup></mrow></math></span> and <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>≥</mo><msub><mi>k</mi><mn>2</mn></msub><mi>s</mi><msup><mrow></mrow><mi>p</mi></msup></mrow></math></span> for all <span><math><mrow><mi>s</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, where <span><math><mrow><msub><mi>k</mi><mn>1</mn></msub><mo>,</mo><msub><mi>k</mi><mn>2</mn></msub><mo>,</mo><mi>p</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mo>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104523"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364265","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 : 2026-04-01Epub Date: 2025-09-16DOI: 10.1016/j.nonrwa.2025.104502
Yaobin Tang, Zhenzhen Li, Binxiang Dai
The paper considers the dynamical behaviors of two competing species for the case of weak competition with nonlocal dispersal and seasonal succession. We first derive the existence and non-existence of traveling waves connecting the trivial equilibrium and the positive periodic solution by using the method of upper-lower solutions and the asymptotic fixed point theorem. Then we obtain the asymptotic spreading properties of the two competing species with compactly supported initial conditions. Our results demonstrate that a competitively weaker species with a faster spreading speed can drive a competitively stronger but slower-spreading species to extinction.
{"title":"Propagation of nonlocal dispersal competition model with seasonal succession","authors":"Yaobin Tang, Zhenzhen Li, Binxiang Dai","doi":"10.1016/j.nonrwa.2025.104502","DOIUrl":"10.1016/j.nonrwa.2025.104502","url":null,"abstract":"<div><div>The paper considers the dynamical behaviors of two competing species for the case of weak competition with nonlocal dispersal and seasonal succession. We first derive the existence and non-existence of traveling waves connecting the trivial equilibrium and the positive periodic solution by using the method of upper-lower solutions and the asymptotic fixed point theorem. Then we obtain the asymptotic spreading properties of the two competing species with compactly supported initial conditions. Our results demonstrate that a competitively weaker species with a faster spreading speed can drive a competitively stronger but slower-spreading species to extinction.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104502"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099450","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}
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