Nonlinear Analysis-Real World Applications最新文献

{"title":"Global well-posedness of full compressible magnetohydrodynamic system in 3D bounded domains with large oscillations and vacuum","authors":"Yazhou Chen ,&nbsp;Yunkun Chen ,&nbsp;Xue Wang","doi":"10.1016/j.nonrwa.2025.104507","DOIUrl":"10.1016/j.nonrwa.2025.104507","url":null,"abstract":"<div><div>The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the magnetic field. For the regular initial data with small energy but possibly large oscillations, the global existence of classical and weak solution as well as the exponential decay rate to the initial-boundary-value problem of this system is obtained. In particular, the density and temperature of such a classical solution are both allowed to vanish initially. Moreover, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly with an exponential rate when the initial vacuum appears (even at a point). Some new observations and useful estimates are developed to overcome the difficulties caused by the slip boundary conditions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104507"},"PeriodicalIF":1.8,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117682","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}

{"title":"On the critical points of planar polynomial Hamiltonian systems","authors":"Anna Cima,&nbsp;Armengol Gasull,&nbsp;Francesc Mañosas","doi":"10.1016/j.nonrwa.2025.104503","DOIUrl":"10.1016/j.nonrwa.2025.104503","url":null,"abstract":"<div><div>It is well known that the critical points of planar polynomial Hamiltonian vector fields are either centers or points with an even number of hyperbolic sectors. We give a sharp upper bound of the number of centers that these systems can have in terms of the degrees of their components. We also prove that generically the critical points at infinity of their Poincaré compactification are either nodes or have indices <span><math><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn></mrow></math></span> or 1 and have at most two sectors: both hyperbolic, both elliptic or one of each type. These characteristics are no more true in the non generic situation. Although these results are known we revisit their proofs. The new proofs are shorter and based on a new approach.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104503"},"PeriodicalIF":1.8,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099838","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}

{"title":"Serrin-type condition for weak solutions to the shear thickening non-Newtonian fluid","authors":"Hyeong-Ohk Bae ,&nbsp;Jörg Wolf","doi":"10.1016/j.nonrwa.2025.104510","DOIUrl":"10.1016/j.nonrwa.2025.104510","url":null,"abstract":"<div><div>In the present paper we consider a weak solution to the equations of shear thickening incompressible fluid. We prove that under a Serrin-type condition imposed on the velocity field <span><math><mi>u</mi></math></span>, the field enjoys a higher integrability properties, which ensures that <span><math><mi>u</mi></math></span> is strong. In particular, we prove that for powers law <span><math><mrow><mi>q</mi><mo>≥</mo><mfrac><mn>11</mn><mn>5</mn></mfrac></mrow></math></span> any weak solution is strong.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104510"},"PeriodicalIF":1.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099443","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}

{"title":"Patterns of dengue and SARS-CoV-2 coinfection in the light of deterministic and stochastic models","authors":"Julia Calatayud ,&nbsp;Marc Jornet ,&nbsp;Carla M.A. Pinto","doi":"10.1016/j.nonrwa.2025.104505","DOIUrl":"10.1016/j.nonrwa.2025.104505","url":null,"abstract":"<div><div>We propose a new mathematical model to capture the overlapping dynamics of dengue and COVID-19 infections in a susceptible population, based on a nonlinear system of ordinary differential equations. First, we calculate the basic reproduction number and present its use in the analysis of outbreaks, long-term dynamics, and parameter sensitivity. Then, we introduce an Itô stochastic version of the system and conduct numerical simulations to explore its behavior, which generalizes the deterministic counterpart. The model is validated with real-world data from Colombia, employing different approaches: global and sub-stages fitting. We describe the emerging challenges, namely, unidentifiable parameters and limited data availability. To simplify the least-squares optimization process, certain parameters were previously fixed. Consequently, the model’s results should be interpreted with caution. Overcoming these limitations will be critical to advance epidemic modeling.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104505"},"PeriodicalIF":1.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099834","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}

{"title":"A p-Laplacian heat equation in a non-cylindrical domain with an oscillating boundary: A homogenization process","authors":"Akambadath Keerthiyil Nandakumaran ,&nbsp;Sankar Kasinathan","doi":"10.1016/j.nonrwa.2025.104501","DOIUrl":"10.1016/j.nonrwa.2025.104501","url":null,"abstract":"<div><div>This article addresses the homogenization of the heat equation involving the <span><math><mi>p</mi></math></span>-Laplacian in non-cylindrical domains with an evolving oscillating boundary. A change of coordinates is employed to transform the heat equations with <span><math><mi>p</mi></math></span>-Laplacian into parabolic <span><math><mi>p</mi></math></span>-Laplacian equations featuring oscillating coefficients in a reference domain. One novelty of this article is that the equation in the reference domain consists of an oscillating coefficient matrix in the nonlinear component, specifically <span><math><msup><mrow><mo>|</mo><msubsup><mi>M</mi><mrow><mrow><mi>ε</mi></mrow></mrow><mrow><mi>t</mi><mi>r</mi></mrow></msubsup><mi>∇</mi><msub><mi>U</mi><mrow><mi>ε</mi></mrow></msub><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup></math></span>. The existence and uniqueness of solutions are demonstrated in the reference domain through a non-trivial Galerkin approximation, accompanied by a significant <span><math><mrow><mi>ε</mi></mrow></math></span>-uniform estimate. On the other hand, a modified two-scale convergence method is employed to derive the two-scale homogenized problem. Furthermore, an explicit solution to the nonlinear cell problem is constructed. This solution is employed to drive the effective equation within the reference domain and corrector result, identified as a transformed effective problem of the heat equation with <span><math><mi>p</mi></math></span>-Laplacian in a non-cylindrical domain featuring an effective evolving boundary.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104501"},"PeriodicalIF":1.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099835","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}

{"title":"Component-wise Krasnosel’skii type fixed point theorem in product spaces and applications","authors":"Laura M. Fernández–Pardo,&nbsp;Jorge Rodríguez–López","doi":"10.1016/j.nonrwa.2025.104506","DOIUrl":"10.1016/j.nonrwa.2025.104506","url":null,"abstract":"<div><div>We present a version of Krasnosel’skiĭ fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index theory in cones, guarantees the existence of a coexistence fixed point, that is, one with nontrivial components. As an application, we prove the existence of periodic solutions with strictly positive components for a system of second-order differential equations. In particular, we address cases involving singular nonlinearities and hybrid terms, characterized by sublinear behavior in one component and superlinear behavior in the other.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104506"},"PeriodicalIF":1.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099837","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}

{"title":"A sufficient condition for absence of mass quantization in a chemotaxis system with local sensing","authors":"Yuri Soga","doi":"10.1016/j.nonrwa.2025.104504","DOIUrl":"10.1016/j.nonrwa.2025.104504","url":null,"abstract":"<div><div>We analyze blowup solutions in infinite time of the Neumann boundary value problem for the fully parabolic chemotaxis system with local sensing:<span><span><span><math><mtable><mtr><mtd><mrow><mo>{</mo><mtable><mtr><mtd><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mrow><mo>(</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>v</mi></mrow></msup><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mspace></mspace><mspace></mspace><mrow><mi>in</mi></mrow><mspace></mspace><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>v</mi><mi>t</mi></msub><mo>=</mo><mstyle><mi>Δ</mi></mstyle><mi>v</mi><mo>−</mo><mi>v</mi><mo>+</mo><mi>u</mi><mspace></mspace><mrow><mi>in</mi></mrow><mspace></mspace><mstyle><mi>Ω</mi></mstyle><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></math></span></span></span>where <span><math><mstyle><mi>Ω</mi></mstyle></math></span> is a ball in two-dimensional space and with nonnegative radially symmetric initial data. In the case of the Keller–Segel system which has similar mathematical structures to our system, it was shown that solutions blow up in finite time if and only if <span><math><mrow><mi>L</mi><mi>log</mi><mi>L</mi></mrow></math></span> for the first component <span><math><mi>u</mi></math></span> diverges in finite time. On the other hand, focusing on the variational structure induced by the signal-dependent motility function <span><math><msup><mi>e</mi><mrow><mo>−</mo><mi>v</mi></mrow></msup></math></span>, we show that the unboundedness of <span><math><mrow><msub><mo>∫</mo><mstyle><mi>Ω</mi></mstyle></msub><msup><mi>e</mi><mi>v</mi></msup><mi>d</mi><mi>x</mi></mrow></math></span> for the second component <span><math><mi>v</mi></math></span> gives rise to blowup solutions in infinite time under the assumption of radial symmetry. Moreover we prove mass concentration phenomena at the origin. It is shown that the radially symmetric solutions of our system develop a singularity like a Dirac delta function in infinite time. Here we investigate the weight of this singularity. Consequently it is shown that mass quantization may not occur; that is, the weight of the singularity can exceed <span><math><mrow><mn>8</mn><mi>π</mi></mrow></math></span> under the assumption of a uniform-in-time lower bound for a Lyapunov functional. This type of behavior cannot be observed in the Keller–Segel system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104504"},"PeriodicalIF":1.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099836","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}

{"title":"Propagation of nonlocal dispersal competition model with seasonal succession","authors":"Yaobin Tang,&nbsp;Zhenzhen Li,&nbsp;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":"2025-09-16","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}

{"title":"Spatial dynamics of a two-strain epidemic model with nonlocal dispersal","authors":"Shi-Ke Hu ,&nbsp;Jiawei Huo ,&nbsp;Rong Yuan ,&nbsp;Hai-Feng Huo","doi":"10.1016/j.nonrwa.2025.104460","DOIUrl":"10.1016/j.nonrwa.2025.104460","url":null,"abstract":"<div><div>This article studies a nonlocal dispersal two-strain epidemic model with Neumann boundary condition in a heterogeneous environment. We define the basic reproduction number for this model and demonstrate that the disease will persist if the basic reproduction number is bigger than one, but will diminish otherwise. We also investigate the competitive exclusion of two strains in various local distributions of transmission and recovery rates. Furthermore, we study the boundedness and existence of the coexist endemic steady-state solution of this model with respect to the nonlocal dispersal rates. Particularly, it is found that, in comparison to the models with random diffusion, two strains with nonlocal dispersal are more liable to coexist, and the disease are more difficult to be controlled via reducing the movement of individuals.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104460"},"PeriodicalIF":1.8,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048421","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}

{"title":"Stationary solutions with vacuum for a hyperbolic–parabolic chemotaxis model in dimension two","authors":"Sophia Hertrich ,&nbsp;Tao Huang ,&nbsp;Diego Yépez ,&nbsp;Kun Zhao","doi":"10.1016/j.nonrwa.2025.104489","DOIUrl":"10.1016/j.nonrwa.2025.104489","url":null,"abstract":"<div><div>In this research, we study the existence of stationary solutions with vacuum to a hyperbolic–parabolic chemotaxis model with nonlinear pressure in dimension two that describes vasculogenesis. We seek radially symmetric solutions in the whole space, in which the system will be reduced to a system of ODE’s on <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span>. The fundamental solutions to the ODE system are the Bessel functions of different types. We find two nontrivial solutions. One is formed by half bump (positive density region) starting at <span><math><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span> and a region of vacuum on the right. Another one is a full nonsymmetric bump away from <span><math><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span>. These solutions bear certain resemblance to <em>in vitro</em> vascular network and the numerically produced structure by Gamba et al. (2003). We also show the nonexistence of full bump starting at <span><math><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span> and nonexistence of full symmetric bump away from <span><math><mrow><mi>r</mi><mo>=</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104489"},"PeriodicalIF":1.8,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019231","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}