Nonlinear Analysis-Real World Applications最新文献

{"title":"On the stability threshold of Couette flow for 2D Boussinesq equations","authors":"Xiaoxia Ren ,&nbsp;Dongyi Wei","doi":"10.1016/j.nonrwa.2025.104421","DOIUrl":"10.1016/j.nonrwa.2025.104421","url":null,"abstract":"<div><div>In this paper, we prove the stability threshold <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> for 2D Boussinesq equations around the Couette flow in <span><math><mrow><mi>T</mi><mo>×</mo><mi>R</mi></mrow></math></span> with Richardson number <span><math><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></math></span>. Here the viscosity <span><math><mi>ν</mi></math></span> and thermal diffusivity <span><math><mi>μ</mi></math></span> can be different. More precisely, if <span><math><mrow><msub><mrow><mo>‖</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>−</mo><mrow><mo>(</mo><mi>y</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></msub><mo>+</mo><msub><mrow><mo>‖</mo><msub><mrow><mi>ρ</mi></mrow><mrow><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><msup><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>y</mi><mo>−</mo><mn>1</mn><mo>‖</mo></mrow><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi><mo>+</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></msub><mo>≤</mo><mi>c</mi><msup><mrow><mrow><mo>(</mo><mo>min</mo><mrow><mo>{</mo><mi>ν</mi><mo>,</mo><mi>μ</mi><mo>}</mo></mrow><mo>)</mo></mrow></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>, <span><math><mrow><mfrac><mrow><mi>ν</mi><mo>+</mo><mi>μ</mi></mrow><mrow><mn>2</mn><mi>γ</mi><msqrt><mrow><mi>ν</mi><mi>μ</mi></mrow></msqrt></mrow></mfrac><mo>&lt;</mo><mn>2</mn><mo>−</mo><mi>ɛ</mi></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>&gt;</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math></span>, then the asymptotic stability holds. Compared with Zhai and Zhao (2023), the regularity assumption is weaker, and the proof is much simpler.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104421"},"PeriodicalIF":1.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144255265","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 well-posedness and spatially inhomogeneous Hopf bifurcation in a predator-prey system with indirect predator-taxis","authors":"Yehu Lv","doi":"10.1016/j.nonrwa.2025.104424","DOIUrl":"10.1016/j.nonrwa.2025.104424","url":null,"abstract":"<div><div>This paper explores a predator-prey system featuring indirect predator-taxis, where prey exhibit a repellent response triggered by chemicals secreted by predator. We first establish the global existence and uniform boundedness of classical solutions for the system in any spatial dimension, assuming that the functional response <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is bounded. Additionally, under the assumption of quadratic decay in the prey population density, we prove the global existence and uniform boundedness of classical solutions for the system in up to two spatial dimensions, assuming that the functional response <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></mrow></math></span> is sublinear. Linear stability analysis reveals that indirect predator-taxis plays a crucial role in pattern formation. For the Lotka-Volterra type functional response, we demonstrate global stability of the positive constant steady state by constructing an appropriate Lyapunov functional. Conversely, for the Beddington-DeAngelis functional response, we investigate Hopf bifurcation in the predator-prey system with indirect predator-taxis. To compute the normal form of this bifurcation, we introduce an efficient new algorithm treating the taxis coefficient as a perturbation parameter. Using this algorithm, we analyze the direction and stability of taxis coefficient-induced Hopf bifurcation. Finally, numerical simulations are conducted to validate our analytical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104424"},"PeriodicalIF":1.8,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144239590","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 attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations","authors":"Beniamin Goldys ,&nbsp;Agus L. Soenjaya ,&nbsp;Thanh Tran","doi":"10.1016/j.nonrwa.2025.104420","DOIUrl":"10.1016/j.nonrwa.2025.104420","url":null,"abstract":"<div><div>We study the long-time behaviour of solutions to some classes of fourth-order nonlinear PDEs with non-monotone nonlinearities, which include the Landau–Lifshitz–Baryakhtar (LLBar) equation (with all relevant fields and spin torques) and the convective Cahn–Hilliard/Allen–Cahn (CH-AC) equation with a proliferation term, in dimensions <span><math><mrow><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>. Firstly, we show the global well-posedness, as well as the existence of global and exponential attractors with finite fractal dimensions for these problems. In the case of the exchange-dominated LLBar equation and the CH-AC equation without convection, an estimate for the rate of convergence of the solution to the corresponding stationary state is given. Finally, we show the existence of a robust family of exponential attractors when <span><math><mrow><mi>d</mi><mo>≤</mo><mn>2</mn></mrow></math></span>. As a corollary, exponential attractor of the LLBar equation is shown to converge to that of the Landau–Lifshitz–Bloch equation in the limit of vanishing exchange damping, while exponential attractor of the convective CH-AC equation is shown to converge to that of the convective Allen–Cahn equation in the limit of vanishing diffusion coefficient.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104420"},"PeriodicalIF":1.8,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196149","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 boundedness in a two-dimensional chemotaxis-Navier–Stokes system with double chemical signals and nonlinear diffusion","authors":"Wang Luo,&nbsp;Zhongping Li","doi":"10.1016/j.nonrwa.2025.104415","DOIUrl":"10.1016/j.nonrwa.2025.104415","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper investigates the following chemotaxis-Navier–Stokes system with double chemical signals and nonlinear diffusion &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;msub&gt;&lt;mrow&gt;&lt;mi&gt;n&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;mi&gt;u&lt;/mi&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&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;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;c&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;mi&gt;u&lt;/mi&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&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;mi&gt;u&lt;/mi&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&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;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&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;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;mi&gt;κ&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;⋅&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;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&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;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;⋅&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&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;in a smooth bounded domain &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&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;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with no-flux/no-flux/no-flux/no-slip boundary conditions, where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;ξ&lt;/mi&gt;&lt;mo&gt;&lt;&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;κ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; are given constants. &lt;span&gt;&lt;math&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is a given function satisfying &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mtext&gt;for all&lt;/mtext&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;We obtain the boundedness of the classical solution to the initial–boundary value problem of the 2D chemotaxis-Navier–Stokes system if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104415"},"PeriodicalIF":1.8,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185531","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 brain tumor growth model with lactate metabolism, viscoelastic effects, and tissue damage","authors":"Giulia Cavalleri ,&nbsp;Pierluigi Colli ,&nbsp;Alain Miranville ,&nbsp;Elisabetta Rocca","doi":"10.1016/j.nonrwa.2025.104419","DOIUrl":"10.1016/j.nonrwa.2025.104419","url":null,"abstract":"<div><div>In this paper, we study a nonlinearly coupled initial–boundary value problem describing the evolution of brain tumor growth, including lactate metabolism. In our modeling approach, we also take into account the viscoelastic properties of the tissues as well as the reversible damage effects that could occur, possibly caused by surgery. After introducing the PDE system, coupling a Fischer–Kolmogorov type equation for the tumor phase with a reaction–diffusion equation for the lactate, a quasi-static momentum balance with nonlinear elasticity and viscosity matrices, and a nonlinear differential inclusion for the damage, we prove the existence of global in time weak solutions under reasonable assumptions on the involved functions and data. Strengthening these assumptions, we subsequently prove further regularity properties of the solutions as well as their continuous dependence with respect to the data, entailing the well-posedness of the Cauchy problem associated with the nonlinear PDE system.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104419"},"PeriodicalIF":1.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178557","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 analysis and numerical simulation of a nonlinear radiofrequency ablation model in cardiac tissue","authors":"Mostafa Bendahmane ,&nbsp;Youssef Ouakrim ,&nbsp;Yassine Ouzrour ,&nbsp;Mohamed Zagour","doi":"10.1016/j.nonrwa.2025.104412","DOIUrl":"10.1016/j.nonrwa.2025.104412","url":null,"abstract":"<div><div>This paper deals with the mathematical analysis and numerical simulation of a new nonlinear ablation system modeling radiofrequency ablation phenomena in cardiac tissue, which incorporates the effects of blood flow on the heat generated when ablation by radiofrequency. The model also considers the effects of viscous energy dissipation. It consists of a coupled thermistor problem and the incompressible Navier–Stokes equations that describe the evolution of temperature, velocity and potential in cardiac tissue. In addition to Faedo–Galerkin method, we use Schauder’s fixed-point theory to prove the existence of the weak solutions in two- and three-dimensional space. Moreover, we prove the uniqueness of the solution under some additional conditions on the data and the solution. Finally, we discuss some numerical results for the validation of the proposed model using the finite element method.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104412"},"PeriodicalIF":1.8,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166243","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":"Existence and global behaviour of solutions of a parabolic problem involving the fractional p-Laplacian in porous medium","authors":"Loïc Constantin,&nbsp;Jacques Giacomoni,&nbsp;Guillaume Warnault","doi":"10.1016/j.nonrwa.2025.104416","DOIUrl":"10.1016/j.nonrwa.2025.104416","url":null,"abstract":"<div><div>In this paper, we prove the existence and the uniqueness of a weak and mild solution of the following nonlinear parabolic problem involving the porous <span><math><mi>p</mi></math></span>-fractional Laplacian: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mi>h</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>m</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mo>)</mo></mrow><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>⋅</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>We also study further the the homogeneous case <span><math><mrow><mi>h</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi></mrow></math></span> with <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. In particular we investigate global time existence, uniqueness, global behaviour of weak solutions and stabilization.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104416"},"PeriodicalIF":1.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166342","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 steady-state solutions of a class of Keller–Segel type models with linear sensitivity and nonlinear consumption rate of chemical stimuli","authors":"Zefu Feng,&nbsp;Luyao Wang","doi":"10.1016/j.nonrwa.2025.104417","DOIUrl":"10.1016/j.nonrwa.2025.104417","url":null,"abstract":"<div><div>This paper is devoted to the study of a class of Keller–Segel type models with Dirichlet boundary conditions and zero-flux boundary conditions on a one-dimensional bounded interval. We show the existence of non-trivial steady state solutions of these models by using sub-super solutions method and standard monotone iteration scheme method. Furthermore, we also show that the steady-state solution of these models is nonlinearly asymptotically stable by using the inverse derivative technique if the initial perturbation is sufficiently small.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104417"},"PeriodicalIF":1.8,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166343","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":"Existence of a weak solution to the Yamabe type flow","authors":"Sitao Zhang","doi":"10.1016/j.nonrwa.2025.104418","DOIUrl":"10.1016/j.nonrwa.2025.104418","url":null,"abstract":"<div><div>In this paper, we study a doubly nonlinear parabolic equation, which is the Yamabe type heat flow on a bounded regular domain in Euclidean space. We show that under suitable assumptions on the initial data <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. We show the existence of a weak solution to the Yamabe type heat flow.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104418"},"PeriodicalIF":1.8,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144154677","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":"Blow-up of a nonlinear reaction–diffusion system with nonlocal weighted exponential boundary condition","authors":"Hongwei Liu ,&nbsp;Lingling Zhang ,&nbsp;Tao Liu","doi":"10.1016/j.nonrwa.2025.104413","DOIUrl":"10.1016/j.nonrwa.2025.104413","url":null,"abstract":"<div><div>In this paper, we study a class of reaction–diffusion system with nonlinear terms, variable coefficients, and nonlocal exponential boundary conditions. We demonstrate the existence of solutions using the subsolution and supersolution method, comparison principle, and representation theorem. Uniqueness of solutions is established via the contraction mapping principle, aided by the Green’s function. Furthermore, we construct supersolutions to prove the existence of global solutions under various conditions. By employing the auxiliary function method, we obtain upper and lower bounds for blow-up solutions under different parametric settings. Finally, examples are provided to verify our theoretical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104413"},"PeriodicalIF":1.8,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124271","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}