{"title":"Asymptotic behavior of thin ferroelectric models","authors":"Kamel Hamdache , Djamila Hamroun","doi":"10.1016/j.nonrwa.2025.104379","DOIUrl":"10.1016/j.nonrwa.2025.104379","url":null,"abstract":"<div><div>It was pointed out in Shaw et al. (2000) that the boundary conditions satisfied by the polarization play an important role in the description of the thin-limit of ferroelectric materials. In this work we confirm the importance of this choice. In the present work, we consider the limiting process as the thickness <span><math><mi>h</mi></math></span> of a thin cylinder of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> goes to 0, and when the polarization satisfies two different boundary conditions. The first type of boundary conditions leads to an in-plane model or <span><math><mrow><mn>2</mn><mi>d</mi><mo>−</mo><mn>2</mn><mi>d</mi></mrow></math></span> configuration while the second one leads to an (in-plane)-(out-of-plane) model for the displacement and the polarization namely a <span><math><mrow><mn>2</mn><mi>d</mi><mo>−</mo><mn>3</mn><mi>d</mi></mrow></math></span> configuration. Moreover, the thin-limit process in both cases induces a change of the Lamé coefficients in the displacement equation, the coupling coefficient between the displacement and polarization equations, the double wells potential of the polarization together to a new contribution in the equation of the out-of-plane component of the polarization for the <span><math><mrow><mn>2</mn><mi>d</mi><mo>−</mo><mn>3</mn><mi>d</mi></mrow></math></span> model. The techniques used rely on a rescaling method that penalizes the out-of-plane variable. Uniform bounds with respect to <span><math><mi>h</mi></math></span> are established, compactness techniques are employed, and the limits of the penalized terms are identified.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104379"},"PeriodicalIF":1.8,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737919","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":"Mass-conserving weak solutions to the continuous nonlinear fragmentation equation in the presence of mass transfer","authors":"Ram Gopal Jaiswal, Ankik Kumar Giri","doi":"10.1016/j.nonrwa.2025.104381","DOIUrl":"10.1016/j.nonrwa.2025.104381","url":null,"abstract":"<div><div>A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the existence of mass-conserving weak solutions to the nonlinear fragmentation equation with mass transfer for collision kernels of the form <span><math><mrow><mi>Φ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mi>κ</mi><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mi>y</mi></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mi>x</mi></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>κ</mi><mo>></mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><msub><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><mn>1</mn></mrow></math></span> for <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>∈</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math></span>, with integrable daughter distribution functions, thereby extending previous results obtained by Giri & Laurençot (2021). In particular, the existence of at least one global weak solution is shown when the collision kernel exhibits at least linear growth, and one local weak solution when the collision kernel exhibits sublinear growth. In both cases, finite superlinear moment bounds are obtained for positive times without requiring the finiteness of initial superlinear moments. Additionally, the uniqueness of solutions is confirmed in both cases.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104381"},"PeriodicalIF":1.8,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737920","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}
Eduardo Abreu , Richard De la cruz , Juan Juajibioy , Wanderson Lambert
{"title":"Weak asymptotic analysis approach for first order scalar conservation laws with nonlocal flux","authors":"Eduardo Abreu , Richard De la cruz , Juan Juajibioy , Wanderson Lambert","doi":"10.1016/j.nonrwa.2025.104378","DOIUrl":"10.1016/j.nonrwa.2025.104378","url":null,"abstract":"<div><div>In this work, we expand on the weak asymptotic analysis originally proposed in Abreu et al. (2024) for the investigation of scalar equations and systems of conservation laws, extending it to encompass scalar equations with nonlocal fluxes. Subsequently, we apply this refined methodology to explore a specific class of nonlocal scalar conservation laws <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>ρ</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>+</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mfenced><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mi>η</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>)</mo></mrow><mi>V</mi><mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>∗</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>)</mo></mrow></mrow></mfenced><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><mi>η</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>η</mi></mrow></msub><mrow><mo>(</mo><mi>⋅</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>η</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>ω</mi><mrow><mo>(</mo><mi>⋅</mi><mo>/</mo><mi>η</mi><mo>)</mo></mrow></mrow></math></span> represents a rescaled asymmetric convolution kernel. Essentially, the extension of the weak asymptotic analysis to nonlocal scalar conservation laws yields a family of approximate solutions that exhibit smoothness in time, local integrability, and essential boundedness in the spatial variable. This notable property facilitates the application of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-compactness arguments, leading to the convergence of a solution family. We further extend the concept of weak asymptotic solutions to a broader class of nonlocal scalar conservation laws by constructing a family of ordinary differential equations, providing a set <span><math><mrow><mo>{</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>η</mi></mrow></msub><mrow><mo>(</mo><mi>⋅</mi><mo>,</mo><mi>ϵ</mi><mo>)</mo></mrow><mo>}</mo></mrow></math></span> of asymptotically approximated solutions. These solutions belong to the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> and, in an asymptotic sense, adhere to Kruzhkov’s entropy inequalities. These characteristics, coupled with a suitable spatial and temporal modulus of continuity (which is independent of <span><math><mi>ϵ</mi></math></span> but dependent on <span><math><mi>η</mi></math></span>, representing the horizon for capturing multiple scales of interactions in the nonlocal model), enable us to extract a subsequence converging to the weak and ","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104378"},"PeriodicalIF":1.8,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734628","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 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, Xiuli Xu, 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, 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>></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 , Lishan Liu , Na Wei , 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 , 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 , 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}
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