Nonlinear Analysis-Real World Applications最新文献

{"title":"Self-similar solutions to a flux-limited Keller–Segel system","authors":"Shohei Kohatsu ,&nbsp;Takasi Senba","doi":"10.1016/j.nonrwa.2024.104308","DOIUrl":"10.1016/j.nonrwa.2024.104308","url":null,"abstract":"<div><div>We consider a flux-limited Keller–Segel system, and construct radial forward self-similar solutions in the critical and super-critical cases, which imply that the system admits global solutions with some rough initial data. We also show existence of radial stationary solutions, and obtain some properties. In order to prove our theorems, we deal with second-order ordinary differential equations of corresponding mass functions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104308"},"PeriodicalIF":1.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180529","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 analytical approach to applying the Lyapunov direct method to an epidemic model with age and stage structures","authors":"Jianquan Li ,&nbsp;Yuming Chen ,&nbsp;Xiaojian Xi ,&nbsp;Nini Xue","doi":"10.1016/j.nonrwa.2024.104312","DOIUrl":"10.1016/j.nonrwa.2024.104312","url":null,"abstract":"<div><div>Usually, it is very challenging to construct appropriate Lyapunov functionals for proving the global stability of age-structured models. In this paper, we propose an analytical approach to applying the Lyapunov direct method for such models. The novelty of this approach lies in successfully handling the two challenges when applying the method. On the one hand, according to the integral terms involved in the model, we propose an easy-to-follow way to determine the kernel functions in the Lyapunov functional candidate. On the other hand, we establish a new integral inequality, which is conducive to arranging the derivative of the functional so that it is easy to see whether the derivative is negative definite or negative semi-definite. As an application, we investigate the global stability of the endemic steady state of an age-structured epidemic model with two infectious stages. Moreover, the Lyapunov functional obtained for the endemic steady state is also helpful for proving the global stability of the disease-free steady state and the persistence of the disease.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104312"},"PeriodicalIF":1.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179290","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 a semilinear pseudo-parabolic equation with nonlinear convolution terms","authors":"Huijie Liu ,&nbsp;Eun-Seok Kim ,&nbsp;Zhong Bo Fang","doi":"10.1016/j.nonrwa.2024.104307","DOIUrl":"10.1016/j.nonrwa.2024.104307","url":null,"abstract":"<div><div>This paper deals with the well-posedness and blow-up phenomena for a semilinear pseudo-parabolic equation with a nonlinear convolution term under the null Dirichlet boundary condition. By Hardy–Littlewood–Sobolev inequality, together with contraction mapping principle and the family of potential wells, we establish the local solvability and obtain the threshold between the existence and nonexistence of the global solution with low initial energy. Meantime, based on the modified differential inequality technique, the results of blow-up with arbitrary initial energy and the upper bound of lifespan are presented.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104307"},"PeriodicalIF":1.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179291","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 limit cycles of a quartic model for Evolutionary Stable Strategies","authors":"Armengol Gasull ,&nbsp;Luiz F.S. Gouveia ,&nbsp;Paulo Santana","doi":"10.1016/j.nonrwa.2024.104313","DOIUrl":"10.1016/j.nonrwa.2024.104313","url":null,"abstract":"<div><div>This paper studies the number of centers and limit cycles of the family of planar quartic polynomial vector fields that has the invariant algebraic curve <span><math><mrow><mrow><mo>(</mo><mn>4</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mn>4</mn><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mrow></math></span> The main interest for this type of vector fields comes from their appearance in some mathematical models in Game Theory composed by two players. In particular, we find examples with five nested limit cycles surrounding the same singularity, as well as examples with four limit cycles formed by two disjoint nests, each one of them with two limit cycles. We also prove a Berlinskiĭ’s type result for this family of vector fields.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104313"},"PeriodicalIF":1.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179292","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 and Hopf Bifurcation for a delayed hand–foot–mouth disease model with continuous age-structure in the exposed class","authors":"Dongxue Yan ,&nbsp;Yongxian Jin ,&nbsp;Hui Cao ,&nbsp;Yu Cao","doi":"10.1016/j.nonrwa.2024.104310","DOIUrl":"10.1016/j.nonrwa.2024.104310","url":null,"abstract":"<div><div>Hand–foot–mouth disease (HFMD) is a mild and highly contagious viral infectious disease common in young children, but anyone can get it. In order to reveal the transmission phenomena of HFMD, we formulate a HFMD model with age structure for latently infected individuals and atime delay. The time delay occurs during the transition from latent to infectious individuals. We reformulate the model as an abstract Cauchy problem and show the presence of equilibria. We specify the basic reproduction number <span><math><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> which determines the threshold dynamics of the HFMD model. For <span><math><mrow><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the disease-free equilibrium <span><math><msub><mrow><mover><mrow><mi>E</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msub></math></span> is globally asymptotically stable. For <span><math><mrow><msub><mrow><mi>ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, we derive that the endemic equilibrium <span><math><msub><mrow><mover><mrow><mi>E</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mo>∗</mo></mrow></msub></math></span> is unstable, which is the criteria for the occurrence of Hopf bifurcation. Finally, some numerical simulations demonstrate the obtained theoretical results and shed light on the impact of time delay on the evolution of HFMD spread.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104310"},"PeriodicalIF":1.8,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180533","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":"Well-posedness of the growth-coagulation equation with singular kernels","authors":"Ankik Kumar Giri ,&nbsp;Philippe Laurençot ,&nbsp;Saroj Si","doi":"10.1016/j.nonrwa.2024.104300","DOIUrl":"10.1016/j.nonrwa.2024.104300","url":null,"abstract":"<div><div>The well-posedness of the growth-coagulation equation is established for coagulation kernels having singularity near the origin and growing at most linearly at infinity. The existence of weak solutions is shown by means of the method of the characteristics and a weak <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-compactness argument. For the existence result, we also show our gratitude to Banach fixed point theorem and a refined version of the Arzelà-Ascoli theorem. In addition, the continuous dependence of solutions upon the initial data is shown with the help of the DiPerna-Lions theory, Gronwall’s inequality and moment estimates. Moreover, the uniqueness of solution follows from the continuous dependence. The results presented in this article extend the contributions made in earlier literature.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104300"},"PeriodicalIF":1.8,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179297","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":"Theoretical investigation on fractal–fractional nonlinear ordinary differential equations","authors":"Abdon Atangana ,&nbsp;Seda İğret Araz","doi":"10.1016/j.nonrwa.2024.104296","DOIUrl":"10.1016/j.nonrwa.2024.104296","url":null,"abstract":"<div><div>In this study, we examine the existence and uniqueness conditions of the solutions of the nonlinear fractal-fractional differential equations. Particular emphasis is placed on four cases: exponential decay, power law, generalized Mittag-Leffler kernels and the Delta-Dirac function. Our first contribution is the formulation of some basic inequalities inspired from Gronwall inequality setting up a solid foundation for our analysis to follow. We subsequently carefully obtain the maximal and minimal solutions in each scenario, providing a complete picture of their structure. Finally we show convergence of four different successive approximation schemes, validating their applicability in the various contexts. This is an important finding that adds to the growing literature on the use of fractional calculus in complex dynamical systems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104296"},"PeriodicalIF":1.8,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179296","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":"Traveling wave solutions of a cholera transmission model with nonlocal diffusion and spatio-temporal delay","authors":"Chenwei Song ,&nbsp;Rui Xu","doi":"10.1016/j.nonrwa.2024.104304","DOIUrl":"10.1016/j.nonrwa.2024.104304","url":null,"abstract":"<div><div>In this paper, we consider the traveling wave solutions of a cholera transmission model with nonlocal diffusion and spatio-temporal delay, in which the discrete delay <span><math><mi>τ</mi></math></span> represents the latent period of cholera and a nonlocal infection term is introduced to describe the impact of infections at all possible locations at time <span><math><mrow><mi>t</mi><mo>−</mo><mi>τ</mi></mrow></math></span> on the current location at time <span><math><mi>t</mi></math></span>. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is calculated by using the method of next generation matrix. In addition, the critical wave speed <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> is established. Firstly, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> and the wave speed <span><math><mrow><mi>c</mi><mo>&gt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, the existence of traveling waves connecting the disease-free steady state and endemic steady state is obtained by using Schauder’s fixed point theorem, the prior estimate, limit theory and suitable Lyapunov functional. By employing a limiting argument, the existence of traveling waves is established when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>c</mi><mo>=</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Secondly, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>c</mi><mo>&lt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, the nonexistence of traveling wave solution is proved by means of two-sided Laplace transform. It is shown that <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> is indeed the minimal wave speed. Numerical simulations are carried out to illustrate the theoretical results. Finally, the impacts of nonlocal diffusion and latent period on minimal wave speed are addressed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104304"},"PeriodicalIF":1.8,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179295","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":"Riemann problem for a nonsymmetric Keyfitz–Kranzer and pressureless gas systems with a time-dependent Coulomb-like friction term","authors":"Richard De la cruz ,&nbsp;Wladimir Neves","doi":"10.1016/j.nonrwa.2024.104301","DOIUrl":"10.1016/j.nonrwa.2024.104301","url":null,"abstract":"<div><div>In this paper, we study the Riemann solutions for two systems: the nonsymmetric Keyfitz–Kranzer system and the pressureless system, both characterized by a time-dependent Coulomb-like friction term. Our analysis identifies two types of Riemann solutions: contact discontinuities and delta-shock solutions. We obtain generalized Rankine–Hugoniot conditions, which support the construction of the delta-shock solution for the nonsymmetric Keyfitz–Kranzer system with a time-dependent Coulomb-like friction term. Furthermore, we demonstrate that as the pressure tends to zero, the Riemann solutions of the nonsymmetric Keyfitz–Kranzer system converge to those of the pressureless system, both incorporating a time-dependent Coulomb-like friction term.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104301"},"PeriodicalIF":1.8,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179294","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 attractors for Moore–Gibson–Thompson thermoelastic extensible beams and Berger plates","authors":"Filippo Dell’Oro ,&nbsp;Lorenzo Liverani ,&nbsp;Vittorino Pata ,&nbsp;Ramon Quintanilla","doi":"10.1016/j.nonrwa.2024.104298","DOIUrl":"10.1016/j.nonrwa.2024.104298","url":null,"abstract":"<div><div>For <span><math><mrow><mi>p</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, and <span><math><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>η</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, we consider an abstract version of the system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>u</mi><mo>−</mo><mrow><mo>(</mo><mrow><mi>p</mi><mo>+</mo><msup><mrow><mo>‖</mo><mo>∇</mo><mi>u</mi><mo>‖</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>η</mi><mi>Δ</mi><mrow><mo>(</mo><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>α</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi><mi>t</mi></mrow></msub><mo>+</mo><mi>α</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>−</mo><mi>β</mi><mi>Δ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>γ</mi><mi>Δ</mi><mi>ϕ</mi><mo>−</mo><mi>δ</mi><mi>Δ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>η</mi><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mspace></mspace></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>describing the dynamics of thermoelastic extensible beams or Berger plates, where the evolution of the temperature is ruled by a regularized Moore–Gibson–Thompson type equation. The existence of a global attractor of optimal regularity is proved.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104298"},"PeriodicalIF":1.8,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143178796","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}