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Adaptive Cucker-Smale networks: Limiting Laplacian time-varying dynamics 自适应cucker - small网络：限制拉普拉斯时变动力学
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-08-01 Epub Date: 2025-12-10 DOI: 10.1016/j.nonrwa.2025.104563
Christian Kuehn , Jaeyoung Yoon
{"title":"Adaptive Cucker-Smale networks: Limiting Laplacian time-varying dynamics","authors":"Christian Kuehn ,&nbsp;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":"2026-08-01","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}
引用次数: 0
A doubly nonlinear parabolic equation with nonlinear perturbation under relaxed growth and exponent conditions 在松弛生长和指数条件下具有非线性摄动的双非线性抛物方程
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-08-01 Epub Date: 2025-11-26 DOI: 10.1016/j.nonrwa.2025.104549
Shun Uchida
{"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":"2026-08-01","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}
引用次数: 0
Local boundedness for minimizers of some non-uniformly polyconvex integrals 一些非一致多凸积分的极小值的局部有界性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-08-01 Epub Date: 2025-12-11 DOI: 10.1016/j.nonrwa.2025.104564
Aiping Zhang, Zesheng Feng, Hongya Gao
{"title":"Local boundedness for minimizers of some non-uniformly polyconvex integrals","authors":"Aiping Zhang,&nbsp;Zesheng Feng,&nbsp;Hongya Gao","doi":"10.1016/j.nonrwa.2025.104564","DOIUrl":"10.1016/j.nonrwa.2025.104564","url":null,"abstract":"<div><div>This paper deals with a class of non-uniformly polyconvex integral functionals with splitting form in 3-dimensional Euclidean space. Under some structural conditions on the energy density, we prove that each component <em>u<sup>α</sup></em> of local minimizer <em>u</em> is locally bounded. Our approach is based on a suitable adaptation of the celebrated De Giorgi’s iterative method, and it relies on an appropriate Caccioppoli-type inequality. Our result can be applied to the polyconvex integral<span><span><span><math><mrow><msub><mo>∫</mo><mstyle><mi>Ω</mi></mstyle></msub><mrow><mo>{</mo><munderover><mo>∑</mo><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mrow><mo>[</mo><mi>λ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo><mi>D</mi></mrow><msup><mi>u</mi><mi>α</mi></msup><msup><mrow><mo>|</mo></mrow><mi>p</mi></msup><mrow><mo>+</mo><mo>|</mo></mrow><msup><mrow><mo>(</mo><msub><mrow><mrow><mi>a</mi></mrow><mi>d</mi><mi>j</mi></mrow><mn>2</mn></msub><mi>D</mi><mi>u</mi><mo>)</mo></mrow><mi>α</mi></msup><msup><mrow><mo>|</mo></mrow><mi>q</mi></msup><msup><mrow><mo>]</mo><mo>+</mo><mo>|</mo><mi>det</mi><mi>D</mi><mi>u</mi><mo>|</mo></mrow><mi>r</mi></msup><mo>+</mo><munderover><mo>∑</mo><mrow><mi>α</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mi>b</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mo>|</mo><msup><mi>u</mi><mi>α</mi></msup><mo>|</mo></mrow><mi>s</mi></msup><mo>}</mo></mrow><mrow><mi>d</mi></mrow><mi>x</mi></mrow></math></span></span></span>with suitable functions <em>λ</em>(<em>x</em>) &gt; 0, <em>b</em>(<em>x</em>) ≥ 0 and exponents <em>p, q</em> &gt; 1, <em>r, s</em> ≥ 1.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"90 ","pages":"Article 104564"},"PeriodicalIF":1.8,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747406","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}
引用次数: 0
Maximal energy dissipation principle and the Riemann problem for shallow water flow: Application to the dam-break problem 浅水水流的最大能量耗散原理和黎曼问题：在溃坝问题中的应用
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-08-01 Epub Date: 2025-12-06 DOI: 10.1016/j.nonrwa.2025.104565
Dalal Daw , Marko Nedeljkov , Sanja Ružičić
{"title":"Maximal energy dissipation principle and the Riemann problem for shallow water flow: Application to the dam-break problem","authors":"Dalal Daw ,&nbsp;Marko Nedeljkov ,&nbsp;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> &lt; 0 and non-negative one for <em>x</em> &gt; 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> &lt; 0 and the bed is dry for <em>x</em> &gt; 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":"2026-08-01","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}
引用次数: 0
Local well-posedness of a coupled Jordan–Moore–Gibson–Thompson–Pennes model of nonlinear ultrasonic heating 非线性超声加热Jordan-Moore-Gibson-Thompson-Pennes耦合模型的局部适定性
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-08-01 Epub Date: 2025-11-26 DOI: 10.1016/j.nonrwa.2025.104546
Imen Benabbas , Belkacem Said-Houari
{"title":"Local well-posedness of a coupled Jordan–Moore–Gibson–Thompson–Pennes model of nonlinear ultrasonic heating","authors":"Imen Benabbas ,&nbsp;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":"2026-08-01","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}
引用次数: 0
Sharp rate of accelerating propagation in a nonlocal model arising in population dynamics 种群动态中产生的非局部模型中加速繁殖的急剧速率
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-06-01 Epub Date: 2025-10-27 DOI: 10.1016/j.nonrwa.2025.104526
Na Li
{"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":"2026-06-01","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}
引用次数: 0
On the control cost via the null controllability concept: The case of an interior set degenerate Schrödinger equation with finite delay 基于零可控性概念的控制代价：有限延迟内集退化Schrödinger方程的情况
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-06-01 Epub Date: 2025-11-08 DOI: 10.1016/j.nonrwa.2025.104532
Mohamed Alahyane , Abderrazak Chrifi , Younes Echarroudi
{"title":"On the control cost via the null controllability concept: The case of an interior set degenerate Schrödinger equation with finite delay","authors":"Mohamed Alahyane ,&nbsp;Abderrazak Chrifi ,&nbsp;Younes Echarroudi","doi":"10.1016/j.nonrwa.2025.104532","DOIUrl":"10.1016/j.nonrwa.2025.104532","url":null,"abstract":"<div><div>In this paper, we are interested in the null controllability property of linear degenerate Schrödinger equation with a finite delay and a degeneracy that occurs in an interior subset of <span><math><mrow><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mtext>i.e</mtext><mspace></mspace><mo>∃</mo><msub><mi>W</mi><mn>1</mn></msub><mo>⊂</mo><mo>⊂</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mtext>such</mtext><mspace></mspace><mtext>that</mtext><mspace></mspace><mo>∀</mo><mi>x</mi><mo>∈</mo><msub><mi>W</mi><mn>1</mn></msub><mo>,</mo><mspace></mspace><mi>k</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mi>k</mi></math></span> stands for quantum diffusion. More precisely, we are looking for a suitable control, called the control time, which steers the studied wave to zero equilibrium in a finite time. To this end, we wield the classical procedure based on a adequate Carleman estimate involving a new weight functions and afterwards we get our observability inequality matched with the full adjoint system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104532"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474422","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}
引用次数: 0
Global bifurcation for a predator-prey system with nonlinear boundary-mediated dispersal 一类具有非线性边界介导扩散的捕食-食饵系统的全局分岔
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-06-01 Epub Date: 2025-11-15 DOI: 10.1016/j.nonrwa.2025.104547
Kaikai Liu , Shangjiang Guo
{"title":"Global bifurcation for a predator-prey system with nonlinear boundary-mediated dispersal","authors":"Kaikai Liu ,&nbsp;Shangjiang Guo","doi":"10.1016/j.nonrwa.2025.104547","DOIUrl":"10.1016/j.nonrwa.2025.104547","url":null,"abstract":"<div><div>This paper presents a complete bifurcation analysis of steady-state solutions for a predator-prey reaction-diffusion-advection system featuring density-dependent boundary conditions. By developing a novel synthesis of local and global bifurcation theories, we characterize the full solution structure emerging from semi-trivial states, revealing how nonlinear boundary terms qualitatively alter system dynamics. Our main results establish: (i) precise conditions for coexistence state bifurcations that coincide with stability transitions of semi-trivial solutions; (ii) complete global continuation of solution branches showing either unbounded persistence or novel connection patterns; and (iii) quantitative criteria for stability thresholds governed by boundary-mediated feedback. The analysis overcomes significant technical challenges through sharp a priori estimates and careful treatment of non-self-adjoint operators arising from the nonlinear boundary conditions. These theoretical advances provide mechanistic explanations for edge effects in ecological systems while developing mathematical tools applicable to broader pattern formation problems. The work opens new directions for studying nonlinear boundary phenomena in biological systems, with natural extensions to multi-species communities and chemotaxis models.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104547"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528541","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}
引用次数: 0
Centers and Lyapunov quantities in a cubic polynomial Kolmogorov differential system 三次多项式Kolmogorov微分系统中的中心和Lyapunov量
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-06-01 Epub Date: 2025-11-09 DOI: 10.1016/j.nonrwa.2025.104536
Jaume Llibre , Zhilin Wang , Dongmei Xiao
{"title":"Centers and Lyapunov quantities in a cubic polynomial Kolmogorov differential system","authors":"Jaume Llibre ,&nbsp;Zhilin Wang ,&nbsp;Dongmei Xiao","doi":"10.1016/j.nonrwa.2025.104536","DOIUrl":"10.1016/j.nonrwa.2025.104536","url":null,"abstract":"<div><div>In this paper we study the center-focus problem for a class of planar cubic polynomial differential system. It is shown that the system has at most two centers, and the center is elementary if the system has a center. Moreover, we characterize the center conditions and show that the maximum order of a weak focus is four if the system has a unique linear center-type equilibrium. And if the system has two linear center-type equilibria, then either the two equilibria are centers or each of them is a weak focus with order one.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104536"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528542","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}
引用次数: 0
Large-time behavior of large solutions to the 2D compressible Navier–Stokes equations with slip boundary conditions 具有滑移边界条件的二维可压缩Navier-Stokes方程大解的大时间行为
IF 1.8 3区 数学
Nonlinear Analysis-Real World Applications Pub Date : 2026-06-01 Epub Date: 2025-10-10 DOI: 10.1016/j.nonrwa.2025.104517
Ying Dai , Ying Sun , Hao Xu
{"title":"Large-time behavior of large solutions to the 2D compressible Navier–Stokes equations with slip boundary conditions","authors":"Ying Dai ,&nbsp;Ying Sun ,&nbsp;Hao Xu","doi":"10.1016/j.nonrwa.2025.104517","DOIUrl":"10.1016/j.nonrwa.2025.104517","url":null,"abstract":"<div><div>This paper is concerned with an initial-boundary value problem of 2D barotropic compressible Navier–Stokes equations subject to slip boundary conditions. Under the assumption that the density is uniformly bounded from above, we study the convergence of the solutions to its associated equilibrium with an exponential decay rate. The analysis is based on the elementary energy methods, the techniques from blow-up criterion and some new estimates for the gradient of velocity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"89 ","pages":"Article 104517"},"PeriodicalIF":1.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145262466","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}
引用次数: 0
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