Nonlinear Analysis-Real World Applications最新文献

{"title":"Stability of planar stationary solution for outflow problem on the viscous vasculogenesis model","authors":"Wenwen Fu,&nbsp;Qingqing Liu","doi":"10.1016/j.nonrwa.2025.104459","DOIUrl":"10.1016/j.nonrwa.2025.104459","url":null,"abstract":"<div><div>In this paper, we are concerned with a hyperbolic–parabolic–elliptic vasculogenesis model in the half-space <span><math><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> under outflow boundary conditions. It is shown that the planar stationary solution is stable with respect to small perturbations in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and the perturbations decay in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span> norm as <span><math><mrow><mi>t</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, provided that the magnitude of the stationary solution is sufficiently small. This result is proved by basic energy estimates. Compared with Navier–Stokes equations, we have effectively dealt with the coupling between the fluid quantities and chemoattractant in the vasculogenesis model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104459"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703763","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":"Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm","authors":"Håkan Andréasson ,&nbsp;Markus Kunze ,&nbsp;Gerhard Rein","doi":"10.1016/j.nonrwa.2025.104467","DOIUrl":"10.1016/j.nonrwa.2025.104467","url":null,"abstract":"<div><div>We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov–Poisson system and to the Einstein–Vlasov system. There are several reasons why a mathematical analysis of this numerical scheme is important. A generalization of the present result to the case of flat axially symmetric solutions would prove that the steady states obtained numerically in Andréasson and Rein (2015) do exist. Moreover, in the relativistic case the question whether a steady state can be obtained by this scheme seems to be related to its dynamical stability. This motivates the desire for a deeper understanding of this strategy.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104467"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713222","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":"2026-04-01","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":"Stability of the Prandtl boundary layer equation under various boundary conditions","authors":"Huashui Zhan","doi":"10.1016/j.nonrwa.2025.104490","DOIUrl":"10.1016/j.nonrwa.2025.104490","url":null,"abstract":"<div><div>By the Crocco transformation, the boundary layer system of the viscous incompressible flow is transferred to a strong degenerate parabolic equation with a nonlinear boundary value condition, referred as the Prandtl boundary layer equation. The key technique in this paper involves applying the reciprocal transformation to convert the Prandtl boundary layer equation into a degenerate parabolic equation in divergent form. The main challenge arises on account of that the reciprocal transformation renders the initial value condition unbounded. To address this, a new unknown function <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is introduced, and the partial differential equation for <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is derived. For this new equation, the existence of these BV entropy solutions are proved by the parabolically regularized method, the maximal value principle is used to obtain the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimate. Under certain restrictions on the data of the Prandtl system, the stability of entropy solutions is demonstrated using different boundary value conditions. Consequently, under the Oleǐnik assumption and the monotonicity condition, the two-dimensional Prandtl boundary layer system is shown to be well-posed through the inverse Crocco transformation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104490"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921984","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":"Integrability and periodic orbits of a 3D jerk system with two quadratic nonlinearities","authors":"Martha Alvarez-Ramírez ,&nbsp;Johanna D. García-Saldaña ,&nbsp;Jaume Llibre","doi":"10.1016/j.nonrwa.2025.104491","DOIUrl":"10.1016/j.nonrwa.2025.104491","url":null,"abstract":"<div><div>In mechanics jerk is the rate of change of an object’s acceleration over time. Thus a jerk equation is a differential equation of the form <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>x</mi></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span> and <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover></math></span> represent the position, velocity, acceleration, and jerk, respectively. The jerk differential equation can be written as the jerk differential system <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>y</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>z</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>z</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper we study the jerk differential system with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>a</mi><mi>x</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mi>y</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, previously studied by other authors showing that this system can exhibit chaos for some values of its parameters. When the parameters <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span> the <span><math><mi>x</mi></math></span>-axis is filled with zero-Hopf equilibria, and all the other orbits are periodic. Here we prove analytically the existence of two families of periodic orbits for sufficiently small values of the parameters <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span>. One family bifurcates from the non-isolated zero-Hopf equilibrium <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>, while the other family bifurcates from a periodic orbit of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104491"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932266","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":"Invasion waves for a class of multi-species non-cooperative systems with nonlocal dispersal","authors":"Wan-Tong Li,&nbsp;Juan Qiu,&nbsp;Ming-Zhen Xin,&nbsp;Xu-Dong Zhao","doi":"10.1016/j.nonrwa.2025.104471","DOIUrl":"10.1016/j.nonrwa.2025.104471","url":null,"abstract":"<div><div>This paper is concerned with the invasion waves for a class of multi-species non-cooperative systems with nonlocal dispersal. We first establish a sharp existence result of the weak traveling wave solution connected the semi-trivial equilibrium for a general multi-species nonlocal dispersal system by Schauder’s fixed-point theorem. And then we apply this result to discuss the traveling wave solutions for a disease-transmission model and a predator–prey model respectively, where we prove that the weak traveling wave solutions connect the positive equilibrium with the help of Lyapunov functional. To get the asymptotic behavior of traveling wave solutions at <span><math><mrow><mo>+</mo><mi>∞</mi></mrow></math></span>, we have to overcome the difficulties brought by the nonlocal dispersal and the non-cooperative of systems themselves.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104471"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144772650","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":"Existence and uniqueness of time-periodic solutions to the Oberbeck–Boussinesq system","authors":"Tomoyuki Nakatsuka","doi":"10.1016/j.nonrwa.2025.104461","DOIUrl":"10.1016/j.nonrwa.2025.104461","url":null,"abstract":"<div><div>This paper is devoted to the study of the time-periodic problem for the Oberbeck–Boussinesq system in the whole space. Our investigation is based on the reformulation of the time-periodic problem and does not depend on the analysis of the initial value problem. We construct a time-periodic solution with more information on its structure than the solutions in preceding studies. We also prove that our solution, small in an appropriate sense, is unique in the class of solutions having slightly more regularity.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104461"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144722113","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":"2026-04-01","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}

{"title":"Extension criterion on the 3D Navier–Stokes equations via partial components in Besov space","authors":"Koji Kanazawa ,&nbsp;Hideo Kozono","doi":"10.1016/j.nonrwa.2025.104458","DOIUrl":"10.1016/j.nonrwa.2025.104458","url":null,"abstract":"<div><div>We find a new extension criterion on the 3D Navier–Stokes equations in terms of horizontal derivatives of the two velocity components in Besov spaces. We shall apply our extension theorem to regularity criterion on weak solutions. Our results generalize the results in the Morrey–Campanato space and Triebel–Lizorkin space by Chen and Gala (2011) and Wei and Li (2014), respectively.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104458"},"PeriodicalIF":1.8,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703762","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":"2026-04-01","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}