Nonlinear Analysis-Real World Applications最新文献

{"title":"Coexistence states for a class of prey–predator models with population flux by attractive transition","authors":"Sheng Xue,&nbsp;Shanbing Li","doi":"10.1016/j.nonrwa.2025.104321","DOIUrl":"10.1016/j.nonrwa.2025.104321","url":null,"abstract":"<div><div>This paper concerns a class of prey–predator models with population flux by attractive transition under homogeneous Dirichlet boundary conditions, which is a modification of the model proposed by Kuto and Odea (Kuto and Oeda, 2022; Oeda and Kuto, 2018). We give the necessary and sufficient conditions for the existence of coexistence states. The mathematical analysis relies on an a priori estimate result and a global bifurcation method. Compared with the previous works (Kuto and Oeda, 2022; Oeda and Kuto, 2018), there are essential differences in establishing an a priori estimate result.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104321"},"PeriodicalIF":1.8,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180038","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":"Junction in a thin multi-domain for nonsimple grade two materials in BH","authors":"Rita Ferreira ,&nbsp;José Matias ,&nbsp;Elvira Zappale","doi":"10.1016/j.nonrwa.2025.104322","DOIUrl":"10.1016/j.nonrwa.2025.104322","url":null,"abstract":"<div><div>We consider a thin multi-domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, with <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, consisting of a vertical rod on top of a horizontal disk made of non-simple grade-two materials or multiphase ones. In this thin multi-domain, we consider a classical hyperelastic energy and complement it by adding an interfacial energy with a bulk density of the kind <span><math><mrow><mi>W</mi><mrow><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>U</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>W</mi></math></span> is a continuous function with linear growth at <span><math><mi>∞</mi></math></span> and <span><math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>U</mi></mrow></math></span> denotes the Hessian tensor of a vector-valued function <span><math><mi>U</mi></math></span> that represents a deformation of the multi-domain. Considering suitable boundary conditions on the admissible deformations and assuming that the two volumes tend to zero at the same rate, we prove that the limit model is well posed in the union of the limit domains, with dimensions 1 and <span><math><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow></math></span>, respectively, and its limiting energy keeps memory of the original full dimensional trace constraints in a more accurate way than previous related models in the literature. Moreover, we show that the limit problem is uncoupled if <span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, and “partially” coupled if <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104322"},"PeriodicalIF":1.8,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180036","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":"An L∞-estimate for solutions to p-Laplacian type equations using an obstacle approach and applications","authors":"Elzon C. Bezerra Júnior ,&nbsp;João Vitor da Silva ,&nbsp;Romário Tomilhero Frias","doi":"10.1016/j.nonrwa.2025.104320","DOIUrl":"10.1016/j.nonrwa.2025.104320","url":null,"abstract":"<div><div>In this paper, we will address a version of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimate for weak solutions of <span><math><mrow><mi>p</mi><mo>−</mo></mrow></math></span>Laplacian type equations of the form <span><span><span><math><mrow><mo>−</mo><mo>div</mo><mi>a</mi><mfenced><mrow><mi>x</mi><mo>,</mo><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span>, <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> (<span><math><mrow><mi>n</mi><mo>⩾</mo><mn>2</mn></mrow></math></span>) is a suitable domain (possibly unbounded with finite measure), <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mi>q</mi><mo>&gt;</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>p</mi></mrow></mfrac></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>≥</mo><mfrac><mrow><mi>p</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></math></span> and <span><math><mrow><mi>a</mi><mo>:</mo><mi>Ω</mi><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> is a continuous vector field satisfying certain structural properties. Unlike the non-variational scenario, our approach is based on analyzing an obstacle problem associated with our equation and exploring its intrinsic qualitative properties. Additionally, in some scenarios, our estimates bring to light new geometric quantities that are not present in the results of the classic literature. At the end, we will present some applications of our estimates, which may be essential in certain contexts of quasi-linear PDEs and related topics.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104320"},"PeriodicalIF":1.8,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180035","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":"Spreading speeds of a delayed noncooperative system in a shifting environment","authors":"Youxi Xie,&nbsp;Guo Lin","doi":"10.1016/j.nonrwa.2025.104324","DOIUrl":"10.1016/j.nonrwa.2025.104324","url":null,"abstract":"<div><div>This article investigates the spreading properties of a noncooperative nonlocal delayed reaction–diffusion system in a shifting environment. It is possible that the system does not satisfy the classical comparison principle for mixed quasimonotone systems. By constructing proper auxiliary equations and utilizing the comparison principle, different spreading speeds are estimated, which depend on the forced speed and the spreading speeds in various limiting equations. These findings are applied to a stage-structured epidemic model, which reveals distinct spreading properties of the susceptible and the infected under different conditions. In particular, the spatial dynamics of the susceptible population, expanding faster than the infected population, generate propagation terraces.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104324"},"PeriodicalIF":1.8,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180037","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":"Local existence of solutions in one-phase Stefan problems for semilinear heat equations using the unified transform method","authors":"Guenbo Hwang","doi":"10.1016/j.nonrwa.2025.104316","DOIUrl":"10.1016/j.nonrwa.2025.104316","url":null,"abstract":"<div><div>We investigate the one-phase Stefan problem for a semilinear heat equation, which plays a pivotal role in understanding phase transitions across diverse media within nonlinear phenomena. Through the application of the unified transform method, commonly referred to as the Fokas method, we derive equivalent nonlinear integral equations to the Stefan problem for the semiliner heat equation. As a result, we establish the local existence and uniqueness of solutions within this framework. The proposed approach not only extends the applicability of the Fokas method to effectively handle Stefan problems, but also provides a direct and efficient analytical method for addressing free boundary value problems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104316"},"PeriodicalIF":1.8,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180034","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":"Mathematical modeling of heat process in a cylindrical domain with nonlinear thermal coefficients and a heat source on the axis","authors":"Julieta Bollati ,&nbsp;Adriana C. Briozzo ,&nbsp;Stanislav N. Kharin ,&nbsp;Targyn A. Nauryz","doi":"10.1016/j.nonrwa.2025.104315","DOIUrl":"10.1016/j.nonrwa.2025.104315","url":null,"abstract":"<div><div>A mathematical model of the heat process in one-dimensional domain which consists of a Stefan problem governed by a cylindrical heat equation with a heat source on the axis <span><math><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></math></span> and nonlinear thermal coefficients is studied. The developed model is particularly applicable for analyzing temperature variations on electrical contact surfaces, where precise thermal management is crucial for ensuring optimal performance and preventing overheating. The use of similarity transformation allows us to obtain an equivalent system of nonlinear integral equations that is solved by applying a fixed point theorem, providing a rigorous mathematical foundation for our analysis.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104315"},"PeriodicalIF":1.8,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180032","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":"Analyticity of solutions to the stationary Navier–Stokes equations via parameter trick","authors":"Hideo Kozono ,&nbsp;Senjo Shimizu","doi":"10.1016/j.nonrwa.2025.104319","DOIUrl":"10.1016/j.nonrwa.2025.104319","url":null,"abstract":"<div><div>We prove analyticity of small solutions to the stationary Navier–Stokes equations in the scaling invariant homogeneous Besov space by using the method of “parameter trick”. This method has been known as an elegant technique for the proof of time–space analyticity of solutions to semi-linear and even quasi-linear parabolic equations. Such a method enables us to apply to the proof for the nonlinear elliptic systems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104319"},"PeriodicalIF":1.8,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180033","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":"Controllability problems of a neutral integro-differential equation with memory","authors":"Sumit Arora,&nbsp;Akambadath Nandakumaran","doi":"10.1016/j.nonrwa.2025.104317","DOIUrl":"10.1016/j.nonrwa.2025.104317","url":null,"abstract":"<div><div>The current study addresses the control problems posed by a semilinear neutral integro-differential equation with memory. The primary objectives of this study are to investigate the existence of a mild solution and approximate controllability of both linear and semilinear control systems in Banach spaces. To accomplish this, we begin by introducing the concept of a resolvent family associated with the homogeneous neutral integro-differential equation without memory. In the process, we establish some important properties of the resolvent family. Subsequently, we develop approximate controllability results for a linear control problem by constructing a linear-quadratic regulator problem. This includes establishing the existence of an optimal pair and determining the expression of the optimal control that produces the approximate controllability of the linear system. Furthermore, we deduce sufficient conditions for the existence of a mild solution and the approximate controllability of a semilinear system in a reflexive Banach space with a uniformly convex dual. Additionally, we delve into the discussion of the approximate controllability for a semilinear problem in general Banach space, assuming a Lipschitz type condition on the nonlinear term. Finally, we implement our findings to examine the approximate controllability of certain partial differential equations, thereby demonstrating their practical relevance.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104317"},"PeriodicalIF":1.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180031","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 priori estimates for the free boundary problem of rotating Euler–Boussinesq equations with surface tension","authors":"Xiaoling Hu","doi":"10.1016/j.nonrwa.2024.104306","DOIUrl":"10.1016/j.nonrwa.2024.104306","url":null,"abstract":"<div><div>In this paper, we adopt the Lagrangian transformation and establish the a <em>priori</em> estimate for solutions to the incompressible rotating Boussinesq equations without velocity dissipation or thermal expansion in a <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> time-dependent domain. By making full use of the gain of regularity for the free-boundary yielded by the existence of surface tension, we release the Taylor-Sign condition attached in [C.C. Hao and W. Zhang, A priori estimates for free boundary problem of 3D incompressible inviscid rotating Boussinesq equations, Z. Angew. Math. Phys., 74(2023), Paper No. 80, 21 pp.].</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104306"},"PeriodicalIF":1.8,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180556","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":"Normal forms of Hopf–Bogdanov–Takens bifurcation for retarded differential equations","authors":"Houssem Achouri ,&nbsp;Chaouki Aouiti","doi":"10.1016/j.nonrwa.2025.104318","DOIUrl":"10.1016/j.nonrwa.2025.104318","url":null,"abstract":"<div><div>This article explores the process of computing normal forms related to a codimension-three Hopf–Bogdanov–Takens (H–B–T) bifurcation in the framework of retarded functional differential equations. The focus is on the behavior of dynamic systems defined by such equations, which exhibit a pair of purely imaginary roots along with a double zero root, referred to as the H–B–T eigenvalue. By employing center manifold reduction alongside the normal form technique, explicit formulas are derived to facilitate the computation of the normal forms for these systems, integrating three parameters for unfolding. To demonstrate the relevance of our results, we apply the analysis to a particular type of bidirectional associative memory network composed of three neurons, where we explore and illustrate the system’s dynamic behavior through an illustrative example and associated numerical simulations.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104318"},"PeriodicalIF":1.8,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180532","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}