Pub Date : 2025-12-10DOI: 10.1016/j.nonrwa.2025.104563
Christian Kuehn , Jaeyoung Yoon
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of the Cucker-Smale and Hegselmann-Krause models to a combined adaptive (or co-evolutionary) network. Reducing our model to a singular limit of fast adaptation, we mathematically analyze the asymptotic behavior of the resulting Laplacian dynamics over various classes of temporal graphs and use these results to explain the behavior of the original proposed adaptive model for fast adaptation. In particular, our approach provides a general methodology for analyzing linear consensus models over time-varying networks that naturally arise as singular limits in many adaptive network models.
{"title":"Adaptive Cucker-Smale networks: Limiting Laplacian time-varying dynamics","authors":"Christian Kuehn , Jaeyoung Yoon","doi":"10.1016/j.nonrwa.2025.104563","DOIUrl":"10.1016/j.nonrwa.2025.104563","url":null,"abstract":"<div><div>Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of the Cucker-Smale and Hegselmann-Krause models to a combined adaptive (or co-evolutionary) network. Reducing our model to a singular limit of fast adaptation, we mathematically analyze the asymptotic behavior of the resulting Laplacian dynamics over various classes of temporal graphs and use these results to explain the behavior of the original proposed adaptive model for fast adaptation. In particular, our approach provides a general methodology for analyzing linear consensus models over time-varying networks that naturally arise as singular limits in many adaptive network models.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104563"},"PeriodicalIF":1.8,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747404","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}
This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at least one strong time-periodic solution, provided the forcing term is time-periodic. The forcing term does not need to satisfy a smallness condition and is allowed to be arbitrarily large.
{"title":"Time-periodic solutions to an energy balance model coupled with an active fluid under arbitrarily large forces","authors":"Gianmarco Del Sarto , Matthias Hieber , Filippo Palma , Tarek Zöchling","doi":"10.1016/j.nonrwa.2025.104558","DOIUrl":"10.1016/j.nonrwa.2025.104558","url":null,"abstract":"<div><div>This article concerns time-periodic solutions to a two-dimensional Sellers-type energy balance model coupled to the three-dimensional primitive equations via a dynamic boundary condition. It is shown that the underlying equations admit at least one strong time-periodic solution, provided the forcing term is time-periodic. The forcing term does not need to satisfy a smallness condition and is allowed to be arbitrarily large.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104558"},"PeriodicalIF":1.8,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747405","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 : 2025-12-06DOI: 10.1016/j.nonrwa.2025.104565
Dalal Daw , Marko Nedeljkov , Sanja Ružičić
The shallow water system with a single discontinuity of the bottom topography is a simple model of a fluid flow with a sudden change in bottom elevation. The discontinuity is modeled by an increasing step function for simplicity and further application to a specific problem. Using an piecewise continuous approximation with the parameter ε ≪ 1 of the step function at , the Riemann problem for the system is transferred after letting ε → 0 into the minimization of energy problem with the constraints: The approximated solution has to satisfy the Dafermos’s maximal dissipation condition around the discontinuity, while shock and rarefaction waves must have non-positive velocity for x < 0 and non-negative one for x > 0. The application of the procedure is made for the dam-break problem with the additional assumptions that fluid is moving from left to right for x < 0 and the bed is dry for x > 0. The existence of an admissible solution corresponds to the dam failure. A shadow wave is a perturbation that consists of two shock waves with an infinitesimally small area between. It is used to model the fluid behavior near the discontinuity.
{"title":"Maximal energy dissipation principle and the Riemann problem for shallow water flow: Application to the dam-break problem","authors":"Dalal Daw , Marko Nedeljkov , Sanja Ružičić","doi":"10.1016/j.nonrwa.2025.104565","DOIUrl":"10.1016/j.nonrwa.2025.104565","url":null,"abstract":"<div><div>The shallow water system with a single discontinuity of the bottom topography is a simple model of a fluid flow with a sudden change in bottom elevation. The discontinuity is modeled by an increasing step function for simplicity and further application to a specific problem. Using an piecewise continuous approximation with the parameter ε ≪ 1 of the step function at <span><math><mrow><mi>x</mi><mo>=</mo><mn>0</mn></mrow></math></span>, the Riemann problem for the system is transferred after letting ε → 0 into the minimization of energy problem with the constraints: The approximated solution has to satisfy the Dafermos’s maximal dissipation condition around the discontinuity, while shock and rarefaction waves must have non-positive velocity for <em>x</em> < 0 and non-negative one for <em>x</em> > 0. The application of the procedure is made for the dam-break problem with the additional assumptions that fluid is moving from left to right for <em>x</em> < 0 and the bed is dry for <em>x</em> > 0. The existence of an admissible solution corresponds to the dam failure. A shadow wave is a perturbation that consists of two shock waves with an infinitesimally small area between. It is used to model the fluid behavior near the discontinuity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104565"},"PeriodicalIF":1.8,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694043","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 : 2025-12-05DOI: 10.1016/j.nonrwa.2025.104559
Yinuo Han , Jianwang Wu , Qian Zhang
<div><div>This paper investigates an attraction-repulsion Navier-Stokes system that incorporates the consumption of chemoattractant and sub-quadratic degradation:<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>n</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>n</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>n</mi><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>n</mi><mi>∇</mi><mi>c</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>n</mi><mi>∇</mi><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>n</mi><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><mrow><msub><mi>c</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>c</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>c</mi><mo>−</mo><mi>c</mi><mi>n</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><mtr><mtd><mrow><msub><mi>w</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>w</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>n</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><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>+</mo><mrow><mo>(</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>u</mi><mo>+</mo><mi>∇</mi><mi>P</mi><mo>+</mo><mi>n</mi><mi>∇</mi><mstyle><mi>Λ</mi></mstyle><mo>,</mo><mspace></mspace><mi>∇</mi><mo>·</mo><mi>u</mi><mo>=</mo><mn>0</mn><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></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>in a bounded and smooth domain <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mn>3</mn></msup></mrow></math></span>, with no-flux/Dirichlet boundary conditions and nonnegative integrable initial data, where <em>f</em> ∈ <em>C</em><sup>1</sup>([0, ∞)) is supposed to generalize standard choices of logistic-type reproduction and degradation, as obtained on letting <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>=</mo><mi>ρ</mi><mi>s</mi><mo>−</mo><mi>μ</mi><msup><mi>s</mi><mi>α</mi></msup></mrow></math></span> for <em>s</em> ≥ 0, with <em>ρ</em> ≥ 0, <em>μ</em> > 0 and <em>α</em> ∈ (1, 2). In this work, it is demonstrated that, in addition to the fundamental condition that <em>f</em>(0) must be nonnegative, the assumption<span><span><span><math><mtable><mtr><mtd><mrow><mfrac><mrow><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mi>s</mi></mfrac><mo>→</mo><mo>−</mo><mi>∞</mi><mspace></mspace><mspace></mspace><mtext>as</mtext><mspace></mspac
{"title":"Global solvability in a 3D attraction-repulsion Navier-Stokes system with consumption of chemoattractant and sub-quadratic degradation","authors":"Yinuo Han , Jianwang Wu , Qian Zhang","doi":"10.1016/j.nonrwa.2025.104559","DOIUrl":"10.1016/j.nonrwa.2025.104559","url":null,"abstract":"<div><div>This paper investigates an attraction-repulsion Navier-Stokes system that incorporates the consumption of chemoattractant and sub-quadratic degradation:<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>n</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>n</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>n</mi><mo>−</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>n</mi><mi>∇</mi><mi>c</mi><mo>)</mo></mrow><mo>+</mo><mi>∇</mi><mo>·</mo><mrow><mo>(</mo><mi>n</mi><mi>∇</mi><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>n</mi><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><mrow><msub><mi>c</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>c</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>c</mi><mo>−</mo><mi>c</mi><mi>n</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><mtr><mtd><mrow><msub><mi>w</mi><mi>t</mi></msub><mo>+</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mi>w</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>w</mi><mo>−</mo><mi>w</mi><mo>+</mo><mi>n</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><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>+</mo><mrow><mo>(</mo><mi>u</mi><mo>·</mo><mi>∇</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>u</mi><mo>+</mo><mi>∇</mi><mi>P</mi><mo>+</mo><mi>n</mi><mi>∇</mi><mstyle><mi>Λ</mi></mstyle><mo>,</mo><mspace></mspace><mi>∇</mi><mo>·</mo><mi>u</mi><mo>=</mo><mn>0</mn><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></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>in a bounded and smooth domain <span><math><mrow><mstyle><mi>Ω</mi></mstyle><mo>⊂</mo><msup><mi>R</mi><mn>3</mn></msup></mrow></math></span>, with no-flux/Dirichlet boundary conditions and nonnegative integrable initial data, where <em>f</em> ∈ <em>C</em><sup>1</sup>([0, ∞)) is supposed to generalize standard choices of logistic-type reproduction and degradation, as obtained on letting <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>=</mo><mi>ρ</mi><mi>s</mi><mo>−</mo><mi>μ</mi><msup><mi>s</mi><mi>α</mi></msup></mrow></math></span> for <em>s</em> ≥ 0, with <em>ρ</em> ≥ 0, <em>μ</em> > 0 and <em>α</em> ∈ (1, 2). In this work, it is demonstrated that, in addition to the fundamental condition that <em>f</em>(0) must be nonnegative, the assumption<span><span><span><math><mtable><mtr><mtd><mrow><mfrac><mrow><mi>f</mi><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mi>s</mi></mfrac><mo>→</mo><mo>−</mo><mi>∞</mi><mspace></mspace><mspace></mspace><mtext>as</mtext><mspace></mspac","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104559"},"PeriodicalIF":1.8,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694044","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 : 2025-12-02DOI: 10.1016/j.nonrwa.2025.104557
Christian Puntini
Starting from the Navier-Stokes equation in the f-plane approximation, we provide an exact and explicit solution of the governing equations at leading order for fluid flows in the upper layer of the ocean at mid-latitudes, driven by a wind stress. Such a solution highlights the presence of a mean Ekman current superimposed to trochoidal oscillations and a background geostrophic current.
{"title":"Nonlinear dynamics of wind-drift currents at mid-latitudes","authors":"Christian Puntini","doi":"10.1016/j.nonrwa.2025.104557","DOIUrl":"10.1016/j.nonrwa.2025.104557","url":null,"abstract":"<div><div>Starting from the Navier-Stokes equation in the <em>f</em>-plane approximation, we provide an exact and explicit solution of the governing equations at leading order for fluid flows in the upper layer of the ocean at mid-latitudes, driven by a wind stress. Such a solution highlights the presence of a mean Ekman current superimposed to trochoidal oscillations and a background geostrophic current.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104557"},"PeriodicalIF":1.8,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693972","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 : 2025-11-26DOI: 10.1016/j.nonrwa.2025.104549
Shun Uchida
In this paper, we consider the initial boundary value problem for a doubly nonlinear parabolic equation with nonlinear perturbation, subject to homogeneous Dirichlet boundary conditions. Our main goal is to relax the growth condition on the nonlinear term and to reduce the constraints on the exponent range, allowing the results to cover both singular and degenerate cases. The proof relies on an L∞-estimate for a time-discrete problem, obtained in earlier work, combined with the L∞-energy method. We also establish uniqueness of solutions under the proposed assumptions.
{"title":"A doubly nonlinear parabolic equation with nonlinear perturbation under relaxed growth and exponent conditions","authors":"Shun Uchida","doi":"10.1016/j.nonrwa.2025.104549","DOIUrl":"10.1016/j.nonrwa.2025.104549","url":null,"abstract":"<div><div>In this paper, we consider the initial boundary value problem for a doubly nonlinear parabolic equation with nonlinear perturbation, subject to homogeneous Dirichlet boundary conditions. Our main goal is to relax the growth condition on the nonlinear term and to reduce the constraints on the exponent range, allowing the results to cover both singular and degenerate cases. The proof relies on an <em>L</em><sup>∞</sup>-estimate for a time-discrete problem, obtained in earlier work, combined with the <em>L</em><sup>∞</sup>-energy method. We also establish uniqueness of solutions under the proposed assumptions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104549"},"PeriodicalIF":1.8,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624201","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 : 2025-11-26DOI: 10.1016/j.nonrwa.2025.104546
Imen Benabbas , Belkacem Said-Houari
In this paper, we analyze a mathematical model of nonlinear ultrasonic heating based on the Jordan–Moore–Gibson–Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using a higher-order energy method together with a fixed-point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is sufficiently short. Moreover, by taking advantage of the uniformity of the derived estimates with respect to the time relaxation parameter τ, we obtain the convergence rate of the solution of the JMGT–Pennes model to the solution of the Westervelt–Pennes model as τ → 0.
{"title":"Local well-posedness of a coupled Jordan–Moore–Gibson–Thompson–Pennes model of nonlinear ultrasonic heating","authors":"Imen Benabbas , Belkacem Said-Houari","doi":"10.1016/j.nonrwa.2025.104546","DOIUrl":"10.1016/j.nonrwa.2025.104546","url":null,"abstract":"<div><div>In this paper, we analyze a mathematical model of nonlinear ultrasonic heating based on the Jordan–Moore–Gibson–Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using a higher-order energy method together with a fixed-point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is sufficiently short. Moreover, by taking advantage of the uniformity of the derived estimates with respect to the time relaxation parameter <em>τ</em>, we obtain the convergence rate of the solution of the JMGT–Pennes model to the solution of the Westervelt–Pennes model as <em>τ</em> → 0.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104546"},"PeriodicalIF":1.8,"publicationDate":"2025-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624200","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 : 2025-11-22DOI: 10.1016/j.nonrwa.2025.104533
Rafael Lima Oliveira , Celene Buriol , Higidio Portillo Oquendo
In this paper, we investigate a coupled system of two equations with distinct characteristics and parameter variations, encompassing relevant scenarios in the study of the asymptotic behavior of solutions. We analyze cases in which the wave-plate system features indirect damping acting exclusively on the wave equation and, alternatively, on the plate equation, while also considering damping in both equations simultaneously. This research establishes the well-posedness of the system, explores the asymptotic behavior (exponential and polynomial decay) of the solutions, and identifies optimal decay rates whenever applicable.
{"title":"Asymptotic behavior for a coupled wave/plate system with fractional memory dissipation","authors":"Rafael Lima Oliveira , Celene Buriol , Higidio Portillo Oquendo","doi":"10.1016/j.nonrwa.2025.104533","DOIUrl":"10.1016/j.nonrwa.2025.104533","url":null,"abstract":"<div><div>In this paper, we investigate a coupled system of two equations with distinct characteristics and parameter variations, encompassing relevant scenarios in the study of the asymptotic behavior of solutions. We analyze cases in which the wave-plate system features indirect damping acting exclusively on the wave equation and, alternatively, on the plate equation, while also considering damping in both equations simultaneously. This research establishes the well-posedness of the system, explores the asymptotic behavior (exponential and polynomial decay) of the solutions, and identifies optimal decay rates whenever applicable.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104533"},"PeriodicalIF":1.8,"publicationDate":"2025-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580234","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 : 2025-11-19DOI: 10.1016/j.nonrwa.2025.104548
Rabiul Hossain, Ishrat Zahan
The selection of an appropriate growth law plays a crucial role in determining species survival in competitive ecological environments, as population density dynamics are strongly influenced by whether growth follows symmetric or non-symmetric patterns. This study investigates a Reaction-Diffusion-Advection (RDA) competition model for two species exposed to harvesting pressure in a spatially heterogeneous domain with no-flux boundary conditions. Two distinct intraspecific growth laws, the classical logistic model and the Gilpin-Ayala model, are incorporated to examine how differing intrinsic biological structures influence competitive outcomes. The primary objective is to analyze spatiotemporal dynamics driven by resource-dependent diffusion-advection strategies and varying harvesting intensities, with particular emphasis on the role of nonlinear intraspecific competition. Using the method of upper and lower solutions together with monotone dynamical system theory, we establish global stability and characterize the long-term behavior of solutions. An implicit-explicit finite difference scheme is employed to study spatial distributions and transient dynamics under varying harvesting intensities and intraspecific competition strengths. The findings elucidate the mechanisms governing competitive exclusion versus species coexistence, highlighting key ecological thresholds that provide new insights into species persistence and competitive outcomes in spatially variable environments.
{"title":"Persistence and extinction of interacting species featuring dissimilar growth functions with harvesting effects: A robust reaction-diffusion-advection model","authors":"Rabiul Hossain, Ishrat Zahan","doi":"10.1016/j.nonrwa.2025.104548","DOIUrl":"10.1016/j.nonrwa.2025.104548","url":null,"abstract":"<div><div>The selection of an appropriate growth law plays a crucial role in determining species survival in competitive ecological environments, as population density dynamics are strongly influenced by whether growth follows symmetric or non-symmetric patterns. This study investigates a Reaction-Diffusion-Advection (RDA) competition model for two species exposed to harvesting pressure in a spatially heterogeneous domain with no-flux boundary conditions. Two distinct intraspecific growth laws, the classical logistic model and the Gilpin-Ayala model, are incorporated to examine how differing intrinsic biological structures influence competitive outcomes. The primary objective is to analyze spatiotemporal dynamics driven by resource-dependent diffusion-advection strategies and varying harvesting intensities, with particular emphasis on the role of nonlinear intraspecific competition. Using the method of upper and lower solutions together with monotone dynamical system theory, we establish global stability and characterize the long-term behavior of solutions. An implicit-explicit finite difference scheme is employed to study spatial distributions and transient dynamics under varying harvesting intensities and intraspecific competition strengths. The findings elucidate the mechanisms governing competitive exclusion versus species coexistence, highlighting key ecological thresholds that provide new insights into species persistence and competitive outcomes in spatially variable environments.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104548"},"PeriodicalIF":1.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145546715","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 : 2025-11-16DOI: 10.1016/j.nonrwa.2025.104545
Fei Wu , Yakui Wu
Cattaneo heat conduction law is a hyperbolic type equation describing the finite speed of heat conduction. Compared to the classical Fourier heat conduction law, Cattaneo’s law provides a more accurate description of heat conduction in materials with high thermal conductivity and short time scales. In this paper, we study the global well-posedness and large-time behavior of the compressible Navier-Stokes-Poisson equations with Cattaneo heat conduction, which is from the dynamic of charged particles. We obtain the optimal time-decay rates of the high-order spatial derivatives of the solution. The decay rates of the solution reveal two conclusions: 1. due to the damping structure of Cattaneo’s law, the heat flux decays to the motionless state at a faster time-decay rate compared with velocity and temperature; 2. the decay rate of heat flux is same as that of density, and the latter has a faster decay rate because of the dispersion effect of the electric field. Finally, we also establish the convergence from the compressible Navier-Stokes-Poisson equations with Cattaneo heat conduction to the classical compressible Navier-Stokes-Poisson equations with Fourier heat conduction.
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