Nonlinear Analysis-Real World Applications最新文献

{"title":"Global solvability of a model for tuberculosis granuloma formation","authors":"Mario Fuest , Johannes Lankeit , Masaaki Mizukami","doi":"10.1016/j.nonrwa.2025.104369","DOIUrl":"10.1016/j.nonrwa.2025.104369","url":null,"abstract":"<div><div>We discuss a nonlinear system of partial differential equations modelling the formation of granuloma during tuberculosis infections and prove the global solvability of the homogeneous Neumann problem for <span><span><span><math><mrow><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>u</mi></mrow></msub><mi>Δ</mi><mi>u</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>u</mi></mrow></msub><mi>u</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>u</mi></mrow></msub><mi>u</mi><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>u</mi></mrow></msub><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>v</mi></mrow></msub><mi>Δ</mi><mi>v</mi><mo>+</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>v</mi></mrow></msub><mi>v</mi><mo>−</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>v</mi></mrow></msub><mi>u</mi><mi>v</mi><mo>+</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>v</mi></mrow></msub><mi>w</mi><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>w</mi></mrow></msub><mi>Δ</mi><mi>w</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mi>w</mi></mrow></msub><mi>u</mi><mi>v</mi><mo>−</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>w</mi></mrow></msub><mi>w</mi><mi>z</mi><mo>−</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>w</mi></mrow></msub><mi>w</mi><mo>,</mo><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>z</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>z</mi></mrow></msub><mi>Δ</mi><mi>z</mi><mo>−</mo><msub><mrow><mi>χ</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>z</mi><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>z</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mi>z</mi><mo>−</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>z</mi></mrow></msub><mi>z</mi><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></mrow></math></span></span></span>in bounded domains in the classical and weak sense in the two- and three-dimensional setting, respectively. In order to derive suitable a priori estimates, we study the evolution of the well-known energy functional for the chemotaxis–consumption system both for the <span><math><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math></span>- and the <span><math><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>)</mo></mrow></math></span>-subsystem. A key challenge compared to “pure” consumption systems consists of overcoming the difficulties raised by the additional, in part positive, terms in the second and third equ","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104369"},"PeriodicalIF":1.8,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715029","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 rarefaction wave for the two-fluid full compressible Navier–Stokes–Poisson system under large initial perturbation","authors":"Qiwei Wu,&nbsp;Xiuli Xu,&nbsp;Jingjun Zhang","doi":"10.1016/j.nonrwa.2025.104380","DOIUrl":"10.1016/j.nonrwa.2025.104380","url":null,"abstract":"<div><div>In this paper, we are concerned with the asymptotic behavior of the solution to the Cauchy problem for the one-dimensional two-fluid full (non-isentropic) compressible Navier–Stokes–Poisson system, which models the motion of viscous charged particles (ions and electrons) in plasmas. The rarefaction wave is shown to be time-asymptotically stable under large initial perturbation as long as the strength of the rarefaction wave is sufficiently small and the adiabatic exponent <span><math><mi>γ</mi></math></span> is close to 1. The proof is based on a delicate energy method, and the key point is to derive the uniform bounds of the density functions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104380"},"PeriodicalIF":1.8,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726208","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":"Global controllability of the Kawahara equation at any time","authors":"Sakil Ahamed,&nbsp;Debanjit Mondal","doi":"10.1016/j.nonrwa.2025.104374","DOIUrl":"10.1016/j.nonrwa.2025.104374","url":null,"abstract":"<div><div>In this article, we prove that the nonlinear Kawahara equation on the periodic domain <span><math><mi>T</mi></math></span> (the unit circle in the plane) is globally approximately controllable in <span><math><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi></mrow></msubsup><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>s</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, at any time <span><math><mrow><mi>T</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, using a two-dimensional control force. The proof is based on the Agrachev–Sarychev approach in geometric control theory.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104374"},"PeriodicalIF":1.8,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726207","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":"Multiple nontrivial solutions for a Kirchhoff-type transmission problem in R3 with concave–convex nonlinearities","authors":"Yuan Gao ,&nbsp;Lishan Liu ,&nbsp;Na Wei ,&nbsp;Yonghong Wu","doi":"10.1016/j.nonrwa.2025.104377","DOIUrl":"10.1016/j.nonrwa.2025.104377","url":null,"abstract":"<div><div>In this paper, by using the fibering map and constrained minimization on the Nehari manifold, we obtain that the Kirchhoff-type transmission problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> with concave-convex nonlinearities has at least two nontrivial solutions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104377"},"PeriodicalIF":1.8,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704070","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":"Convergence of solutions for a four-species food chain model with decaying disturbances","authors":"Jitsuro Sugié","doi":"10.1016/j.nonrwa.2025.104372","DOIUrl":"10.1016/j.nonrwa.2025.104372","url":null,"abstract":"<div><div>Ecosystems are significantly impacted by both natural and anthropogenic disturbances. This study utilizes a four-species ecosystem model to examine the asymptotic behavior of the population densities of each species, particularly the uniform boundedness of the solutions and the convergence of all solutions to an interior point. Considering the effects of disturbances, a system of differential equations with time-varying coefficients is employed to describe the mathematical model. If the magnitude and persistence of disturbances are substantial, the ecosystem may be destroyed, leading to species extinction. Thus, this study assumes that the effects of disturbances gradually diminish, depending on species adaptability and environmental resilience. This assumption is modeled using absolutely integrable time-varying coefficients. If all solutions converge to an interior point, all species coexistence within the ecosystem is achieved. Consequently, this study provides sufficient conditions for the permanence of the model. Moreover, in the scenario where the time-varying coefficients are not absolutely integrable, the potential for species extinction and survival is analyzed using a three-species ecosystem model.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104372"},"PeriodicalIF":1.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143697361","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":"Zero-electron-mass limit for Euler–Poisson system in a bounded domain","authors":"Qiangchang Ju ,&nbsp;Cunming Liu","doi":"10.1016/j.nonrwa.2025.104376","DOIUrl":"10.1016/j.nonrwa.2025.104376","url":null,"abstract":"<div><div>In this paper, we study the zero-electron-mass limit of Euler–Poisson system in a bounded domain with an insulating boundary condition. The limit was only verified for the domain with no boundary in previous works. By approximation techniques, we establish the local well-posedness of classical solutions to the initial boundary value problem in the mixed space–time Sobolev space for the fixed parameter. Then, the local convergence of the system to the incompressible Euler equations with damping is proved rigorously for general initial data. Furthermore, the global convergence of smooth solutions is also justified for small initial data.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104376"},"PeriodicalIF":1.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680446","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":"Variational approach to the periodic problem for a nonlinear parabolic equation in Musielak–Orlicz spaces","authors":"A. Nowakowski ,&nbsp;E. Öztürk","doi":"10.1016/j.nonrwa.2025.104375","DOIUrl":"10.1016/j.nonrwa.2025.104375","url":null,"abstract":"<div><div>We discuss the periodic problem for a nonlinear parabolic equation of the form: <span><span><span>(1)</span><span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>t</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>−</mo><mi>A</mi><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>x</mi></mrow></msub><mfenced><mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfenced><mo>−</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>x</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span></span></span>where <span><math><mi>A</mi></math></span> is a nonlinear operator in a generalized modular space; <span><math><mi>H</mi></math></span> and <span><math><mi>Q</mi></math></span> are convex functionals. We derive a new variational method based on the Fenchel–Young conjugacy to prove the existence of periodic solutions. Next, we apply the abstract result to a nonlinear parabolic equation in Musielak–Orlicz spaces.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104375"},"PeriodicalIF":1.8,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680445","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":"Riemannian starshape and capacitary problems","authors":"Kazuhiro Ishige ,&nbsp;Paolo Salani ,&nbsp;Asuka Takatsu","doi":"10.1016/j.nonrwa.2025.104368","DOIUrl":"10.1016/j.nonrwa.2025.104368","url":null,"abstract":"<div><div>We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restrict ourselves to starshaped rings in a warped product of an open interval and the unit sphere. We also extend the result by replacing the Laplacian with the <span><math><mi>q</mi></math></span>-Laplacian.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104368"},"PeriodicalIF":1.8,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Γ-convergence involving nonlocal gradients with varying horizon: Recovery of local and fractional models","authors":"Javier Cueto ,&nbsp;Carolin Kreisbeck ,&nbsp;Hidde Schönberger","doi":"10.1016/j.nonrwa.2025.104371","DOIUrl":"10.1016/j.nonrwa.2025.104371","url":null,"abstract":"<div><div>This work revolves around the rigorous asymptotic analysis of models in nonlocal hyperelasticity. The corresponding variational problems involve integral functionals depending on nonlocal gradients with a finite interaction range <span><math><mi>δ</mi></math></span>, called the horizon. After an isotropic scaling of the associated kernel functions, we prove convergence results in the two critical limit regimes of vanishing and diverging horizon. While the nonlocal gradients localize to the classical gradient as <span><math><mrow><mi>δ</mi><mo>→</mo><mn>0</mn></mrow></math></span>, we recover the Riesz fractional gradient as <span><math><mrow><mi>δ</mi><mo>→</mo><mi>∞</mi></mrow></math></span>, irrespective of the nonlocal gradient we started with. Besides rigorous convergence statements for the nonlocal gradients, our analysis in both cases requires compact embeddings uniformly in <span><math><mi>δ</mi></math></span> as a crucial ingredient. These tools enable us to derive the <span><math><mi>Γ</mi></math></span>-convergence of quasiconvex integral functionals with varying horizon to their local and fractional counterparts, respectively.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104371"},"PeriodicalIF":1.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Note on global stability of 2D anisotropic Boussinesq equations near the hydrostatic equilibrium","authors":"Hua Qiu,&nbsp;Xia Wang","doi":"10.1016/j.nonrwa.2025.104370","DOIUrl":"10.1016/j.nonrwa.2025.104370","url":null,"abstract":"<div><div>In this note, we consider the stability problem of the 2D anisotropic Boussinesq equations near the hydrostatic equilibrium. Precisely, we obtain the global stability of smooth solution for the 2D Boussinesq equations with partial dissipation and horizontal diffusion in sense of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Our result extends the recent stability results in Ji et al., (2019), Wei et al., (2021), Chen and Liu (2022).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104370"},"PeriodicalIF":1.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143680442","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}