Nonlinear Analysis-Real World Applications最新文献

{"title":"Sustained oscillations in an age-structured predator–prey model incorporating time delay","authors":"Kaidi Cao ,&nbsp;Yajing Li ,&nbsp;Zhihua Liu","doi":"10.1016/j.nonrwa.2024.104303","DOIUrl":"10.1016/j.nonrwa.2024.104303","url":null,"abstract":"<div><div>Recent studies of the predator–prey model in theoretical ecology have found that their interactions are not only limited by the predator–prey reaction time delay <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> but also controlled by the predator development time <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Based on this fact, we explore and analyze the effect of double time delays on the predator–prey model. Under the influence of the complexity of the biological environment, a new ratio-dependent functional response is used to reflect the relationship between prey and predator. We explore the equilibrium state and linearized equations of the system, incorporating the characteristic equations of positive equilibrium state and the global stability of boundary equilibrium. Moreover, our mathematical analyses show that when the parameters <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are changed independently, the system exhibits the stable switching curves and Hopf bifurcation at the positive equilibrium state. In the case of <span><math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>, there are also sustained periodic oscillations. Ultimately, detail numerical simulations are used to verify the theoretical results and a simple summary is presented.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104303"},"PeriodicalIF":1.8,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180531","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 host-pathogen coevolution model, Part I: Run straight for your life","authors":"Matthieu Alfaro ,&nbsp;Florian Lavigne ,&nbsp;Lionel Roques","doi":"10.1016/j.nonrwa.2024.104305","DOIUrl":"10.1016/j.nonrwa.2024.104305","url":null,"abstract":"<div><div>In this study, we propose a novel model describing the coevolution between hosts and pathogens, based on a non-local partial differential equation formalism for populations structured by phenotypic traits. Our objective with this model is to illustrate scenarios corresponding to the evolutionary concept of “Chase Red Queen scenario”, characterized by perpetual evolutionary chases between hosts and pathogens. First, numerical simulations show the emergence of such scenarios, depicting the escape of the host (in phenotypic space) pursued by the pathogen. We observe two types of behaviors, depending on the assumption about the presence of a phenotypic optimum for the host: either the formation of traveling pulses moving along a straight line with constant speed and constant profiles, or stable phenotypic distributions that periodically rotate along a circle in the phenotypic space. Through rigorous perturbation techniques and careful application of the implicit function theorem in rather intricate function spaces, we demonstrate the existence of the first type of behavior, namely traveling pulses moving with constant speed along a straight line. Just as the Lotka–Volterra models have revealed periodic dynamics without the need for environmental forcing, our work shows that, from the pathogen’s point of view, various trajectories of mobile optima can emerge from coevolution with a host species.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104305"},"PeriodicalIF":1.8,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180530","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":"Logistic damping effect in a chemotaxis system with density-suppressed motility and indirect signal consumption","authors":"Quanyong Zhao,&nbsp;Jinrong Wang","doi":"10.1016/j.nonrwa.2024.104314","DOIUrl":"10.1016/j.nonrwa.2024.104314","url":null,"abstract":"<div><div>In this paper, we study the following chemotaxis model <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mrow><mo>(</mo><mi>φ</mi><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>r</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>l</mi></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>v</mi><mi>w</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>δ</mi><mi>w</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>under homogeneous Neumann boundary conditions in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary, where the parameters <span><math><mi>δ</mi></math></span>, <span><math><mrow><mi>μ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>r</mi><mo>∈</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><mi>l</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. The positive motility function satisfies <span><math><mrow><mi>φ</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup><mrow><mo>(</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span>, and the purpose of this paper is to weaken the restriction on <span><math><mi>l</mi></math></span> which ensures the existence of global bounded solutions Li et al. (2022). It was shown that when <span><math><mrow><mi>n</mi><mo>≤</mo><mn>3</mn></mrow></math></span>, there exists a global bounded classical solution for all <span><math><mrow><mi>l</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. When <span><math><mrow><mi>n</mi><mo>≥</mo><mn>4</mn></mrow></math></span>, then we concluded that the system admits a global bounded classical solution for all <span><math><mrow><mi>l</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>, and that the sufficiently large <span><math><mi>μ</mi></math></span> can ensure the existence of global bounded solutions if <span><math><mrow><mi>l</mi><mo>=</mo><mn>2</mn></mrow></math></span>. Moreover, we also studied the large time behavior of solutions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104314"},"PeriodicalIF":1.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180551","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":"Boundedness and finite-time blow-up in a quasilinear chemotaxis system with space dependent logistic source and nonlinear production","authors":"Neng Zhu ,&nbsp;Wanwan Wang","doi":"10.1016/j.nonrwa.2024.104309","DOIUrl":"10.1016/j.nonrwa.2024.104309","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper is concerned with the following quasilinear chemotaxis system with space dependent logistic source and nonlinear production &lt;span&gt;&lt;span&gt;&lt;span&gt;(&lt;span&gt;&lt;math&gt;&lt;mo&gt;⋆&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;)&lt;/span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;φ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;ψ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;with homogeneous Neumann boundary conditions, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;⩾&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Here &lt;span&gt;&lt;math&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; are continuous positive functions, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;κ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; has a positive lower bound, the nonlinear diffusivity &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;φ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/m","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104309"},"PeriodicalIF":1.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179300","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":"Adaptive control for nonlinear cyber–physical systems in the presence of actuator attacks","authors":"Wassim M. Haddad ,&nbsp;Dhruva Venkat ,&nbsp;Tansel Yucelen ,&nbsp;Mark S. Whorton","doi":"10.1016/j.nonrwa.2024.104302","DOIUrl":"10.1016/j.nonrwa.2024.104302","url":null,"abstract":"<div><div>In this paper, we consider time-varying multiplicative and additive actuator attacks for nonlinear cyber–physical systems and present an adaptive control architecture to suppress the effect of these attacks. The control architecture consists of a nominal controller and an adaptive corrective block that is used to modify the output of the nominal controller in the presence of the actuator attacks. It is shown that the closed-loop system remains uniformly ultimately bounded in the face of time-varying multiplicative and additive actuator attacks avoiding the need for a separate attack detection unit. In the case when the attacks are constant our adaptive control architecture guarantees partial asymptotic stability of the closed-loop system. Simulation results corresponding to the controlled dynamics of a flexible link robot, the controlled lateral directional dynamics of an aircraft, as well as a controlled axial flow compression system subjected to actuator attacks are provided to demonstrate the efficacy of the proposed approach.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104302"},"PeriodicalIF":1.8,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179299","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 existence and boundedness in a chemotaxis-convection model with sensitivity functions for tumor angiogenesis","authors":"Yutaro Chiyo ,&nbsp;Masaaki Mizukami","doi":"10.1016/j.nonrwa.2024.104311","DOIUrl":"10.1016/j.nonrwa.2024.104311","url":null,"abstract":"<div><div>This paper deals with the fully parabolic chemotaxis-convection model with sensitivity functions for tumor angiogenesis, <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>+</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>v</mi><mi>ξ</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>∇</mo><mi>w</mi><mo>)</mo></mrow><mo>+</mo><mi>α</mi><mi>u</mi><mo>−</mo><mi>β</mi><mi>v</mi><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>w</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>w</mi><mo>+</mo><mi>γ</mi><mi>u</mi><mo>−</mo><mi>δ</mi><mi>w</mi><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>under homogeneous Neumann boundary conditions and initial conditions, where <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><mo>(</mo><mi>n</mi><mo>≤</mo><mn>3</mn><mo>)</mo></mrow></math></span> is a bounded domain with smooth boundary, <span><math><mrow><msub><mrow><mi>χ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>χ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>ξ</mi></mrow></math></span> are functions satisfying some conditions and <span><math><mrow><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>,</mo><mi>δ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> are constants. The purpose of this paper is to establish global existence and boundedness in this system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104311"},"PeriodicalIF":1.8,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143179298","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":"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}