Journal of Mathematical Analysis and Applications最新文献

{"title":"On elliptic equations with unbounded or decaying potentials involving Stein-Weiss convolution parts and critical exponential growth","authors":"Claudianor Oliveira Alves ,&nbsp;Manassés de Souza ,&nbsp;Liejun Shen","doi":"10.1016/j.jmaa.2025.129483","DOIUrl":"10.1016/j.jmaa.2025.129483","url":null,"abstract":"<div><div>We study a class of nonlinear Schrödinger equations with Stein-Weiss convolution parts<span><span><span><math><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo><mi>u</mi><mo>=</mo><mrow><mo>(</mo><munder><mo>∫</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></munder><mfrac><mrow><mi>F</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>μ</mi></mrow></msup><mo>|</mo><mo>|</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mi>d</mi><mi>y</mi><mo>)</mo></mrow><mfrac><mrow><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>β</mi></mrow></msup></mrow></mfrac><mo>,</mo><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></math></span></span></span> where <em>V</em> is an unbounded or decaying potential, <span><math><mi>β</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span> with <span><math><mn>0</mn><mo>&lt;</mo><mn>2</mn><mi>β</mi><mo>+</mo><mi>μ</mi><mo>&lt;</mo><mn>2</mn></math></span>, and <em>F</em> denotes the primitive of <em>f</em> that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. Via establishing a new version of the Trudinger-Moser inequality, we shall exploit the general minimax principle to demonstrate the existence of nontrivial solutions using variational method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129483"},"PeriodicalIF":1.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644541","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 (μ,ν)-dichotomy spectrum","authors":"Lucas Backes","doi":"10.1016/j.jmaa.2025.129482","DOIUrl":"10.1016/j.jmaa.2025.129482","url":null,"abstract":"<div><div>In this work, we introduce three notions of dichotomy spectrum based on general growth rates and describe their structure. Our results are applicable to nonautonomous linear systems acting on general Banach spaces having negative <em>μ</em>-index of compactness, a condition which is satisfied, for instance, by any sequence of compact operators. Moreover, for any possible form of the spectra, we present an explicit example exhibiting such spectrum. Furthermore, as an application, we obtain normal forms of certain nonautonomous systems. We emphasize that the classical Sacker-Sell spectrum can be obtained as a very particular case of our setting.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129482"},"PeriodicalIF":1.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644542","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":"The Fueter Mittag-Leffler Bargmann transform","authors":"Natanael Alpay ,&nbsp;Antonino De Martino ,&nbsp;Kamal Diki","doi":"10.1016/j.jmaa.2025.129480","DOIUrl":"10.1016/j.jmaa.2025.129480","url":null,"abstract":"<div><div>In this paper we continue exploring the Mittag-Leffler Bargmann (MLB) transform, which maps the Hilbert space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>)</mo></math></span> onto the Mittag-Leffler-Fock (MLF) space. The MLF space is a reproducing kernel Hilbert space that extends the classic Fock space and its reproducing kernel is given by the Mittag-Leffler function. We study the MLB transform and its main properties in the quaternionic setting. In this noncommutative setting there are two function theories that are prominent: the slice hyperholomorphic theory and the Fueter regular theory. The connection between the slice hyperholomorphic functions and the Fueter regular functions is given by the Fueter mapping theorem. The Mittag-Leffler Bargmann transform investigated in this paper maps the quaternionic-valued <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>R</mi><mo>,</mo><mi>H</mi><mo>)</mo></math></span> space onto a counterpart of the MLF space in the Fueter regular setting. Finally the creation, annihilation, backward-shift and integration operators are studied in the case of the Fueter-MLF space.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129480"},"PeriodicalIF":1.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684952","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}

{"title":"Spherically symmetric strong solution of compressible flow with large data and density-dependent viscosities","authors":"Xueyao Zhang","doi":"10.1016/j.jmaa.2025.129488","DOIUrl":"10.1016/j.jmaa.2025.129488","url":null,"abstract":"<div><div>We consider the isentropic compressible Navier-Stokes equations with density-dependent viscosities <span><math><mi>μ</mi><mo>(</mo><mi>ρ</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span>, <span><math><mi>λ</mi><mo>(</mo><mi>ρ</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>α</mi><mo>−</mo><mn>1</mn><mo>)</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>α</mi></mrow></msup></math></span> in <em>N</em>-dimensional (<span><math><mi>N</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>) bounded domain when the initial data are spherically symmetric. Based on the exploitation of the one-dimensional and non-swirl feature of symmetric solution, together with the BD-entropy estimates, the global well-posedness of strong solution with the symmetry center is proved for non-vacuum and large initial data as <span><math><mi>N</mi><mo>=</mo><mn>2</mn></math></span>, <span><math><mfrac><mrow><mn>4</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>≤</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>γ</mi></math></span> or <span><math><mi>N</mi><mo>=</mo><mn>3</mn></math></span>, <span><math><mfrac><mrow><mn>7</mn></mrow><mrow><mn>8</mn></mrow></mfrac><mo>≤</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></math></span>, <span><math><mn>1</mn><mo>&lt;</mo><mi>γ</mi><mo>&lt;</mo><mn>9</mn><mi>α</mi><mo>−</mo><mn>6</mn></math></span>. In particular, it is shown that the solution will not develop the vacuum states in any finite time provided that no vacuum states are present initially.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129488"},"PeriodicalIF":1.2,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644592","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 algebras with locally convex topologies admitting Arens products in their second topological duals","authors":"M. Filali ,&nbsp;M. Sangani Monfared","doi":"10.1016/j.jmaa.2025.129477","DOIUrl":"10.1016/j.jmaa.2025.129477","url":null,"abstract":"<div><div>We study algebras with locally convex topologies admitting Arens products in their second topological duals. We identify the exact conditions required for the existence of Arens products. We show that for algebras admitting Arens products in their second duals, the identity <span><math><mi>W</mi><mi>A</mi><mi>P</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> is equivalent to Arens regularity (Pym's criterion). We show that on any infinite dimensional normed algebra <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>)</mo></math></span>, there exist uncountably many locally convex topologies <em>τ</em> compatible with the duality <span><math><mo>〈</mo><mi>A</mi><mo>,</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>〉</mo></math></span>, such that <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math></span> admits Arens products in its second topological dual. If <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mo>‖</mo><mo>⋅</mo><mo>‖</mo><mo>)</mo></math></span> is Arens regular, strongly Arens irregular or extremely non-Arens regular, then there are uncountably many locally convex topologies <em>τ</em> on <em>A</em> for which <span><math><mo>(</mo><mi>A</mi><mo>,</mo><mi>τ</mi><mo>)</mo></math></span> has the same property.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129477"},"PeriodicalIF":1.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143644704","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":"Normalized solutions for the mass supercritical Kirchhoff problem","authors":"Liu Gao,&nbsp;Zhong Tan","doi":"10.1016/j.jmaa.2025.129475","DOIUrl":"10.1016/j.jmaa.2025.129475","url":null,"abstract":"<div><div>In the present paper, we are concerned with the existence of normalized solutions for the Kirchhoff problem, where the nonlinear term exhibits some new weak mass supercritical conditions. By employing analytical techniques and critical point theorems, we establish several new existence results. Our main results improve and complement the works of He et al. <span><span>[10]</span></span>, Wang and Qian (2023) <span><span>[22]</span></span> and some other related literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129475"},"PeriodicalIF":1.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636628","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":"Analysis of SIS infectious disease dynamics with linear external sources and free boundaries: A computational and theoretical perspective","authors":"Yarong Zhang ,&nbsp;Meng Hu ,&nbsp;Jie Zheng ,&nbsp;Xinyu Shi","doi":"10.1016/j.jmaa.2025.129448","DOIUrl":"10.1016/j.jmaa.2025.129448","url":null,"abstract":"<div><div>The spatio-temporal distribution of individuals within the SIS (Susceptible-Infected-Susceptible) model is pivotal for the effective prevention and control of infectious diseases. This study leverages the reaction-diffusion epidemic model to improve the accuracy of identifying infected areas and predicting potential outbreaks. Compression mapping and the standard theory of parabolic equations are applied to analyze the dynamics of susceptible individuals influenced by linear external sources, simulating their birth and death rates. Key findings reveal a dichotomous relationship between the spread and extinction of infectious diseases, dictated by the time-dependent basic reproduction number. Furthermore, the study investigates the impact of the diffusion coefficient, the propagation potential of infected individuals, and the initial infection range on disease dissemination or attenuation. Numerical simulations support the theoretical findings, indicating that a high expanding capacity of infected individuals poses challenges to effective disease prevention and control. This work provides novel insights into the spatio-temporal dynamics of the SIS model and lays a foundation for future research endeavours in this domain.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129448"},"PeriodicalIF":1.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143621372","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 and global properties of spaces of minimal usco maps","authors":"Serhii Bardyla ,&nbsp;Branislav Novotný ,&nbsp;Jaroslav Šupina","doi":"10.1016/j.jmaa.2025.129472","DOIUrl":"10.1016/j.jmaa.2025.129472","url":null,"abstract":"<div><div>In this paper, we study an interplay between local and global properties of spaces of minimal usco maps equipped with the topology of uniform convergence on compact sets. In particular, for each locally compact space <em>X</em> and metric space <em>Y</em>, we characterize the space of minimal usco maps from <em>X</em> to <em>Y</em>, satisfying one of the following properties: (i) compact, (ii) locally compact, (iii) <em>σ</em>-compact, (iv) locally <em>σ</em>-compact, (v) metrizable, (vi) ccc, (vii) locally ccc, where in the last two items we additionally assumed that <em>Y</em> is separable and non-discrete. Some of the aforementioned results complement ones of Ľubica Holá and Dušan Holý. Also, we obtain analogous characterizations for spaces of minimal cusco maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129472"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637087","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}

{"title":"Boundedness and global existence in a higher-dimensional parabolic-elliptic-ODE chemotaxis-haptotaxis model with remodeling of non-diffusible attractant","authors":"Ling Liu","doi":"10.1016/j.jmaa.2025.129473","DOIUrl":"10.1016/j.jmaa.2025.129473","url":null,"abstract":"<div><div>This paper addresses the issue of boundedness for solutions to the following quasilinear chemotaxis-haptotaxis model of parabolic-elliptic-ODE type:<span><span><span><math><mrow><mo>{</mo><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><mi>χ</mi><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>)</mo><mo>−</mo><mi>ξ</mi><mi>∇</mi><mo>⋅</mo><mo>(</mo><mi>u</mi><mi>∇</mi><mi>w</mi><mo>)</mo><mo>+</mo><mi>u</mi><mo>(</mo><mi>r</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><mi>w</mi><mo>)</mo><mo>,</mo><mspace></mspace><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><mn>0</mn><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>u</mi><mo>−</mo><mi>v</mi><mo>,</mo><mspace></mspace><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>v</mi><mi>w</mi><mo>+</mo><mi>η</mi><mi>w</mi><mo>(</mo><mn>1</mn><mo>−</mo><mi>u</mi><mo>−</mo><mi>w</mi><mo>)</mo><mo>,</mo><mspace></mspace><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></math></span></span></span> subject to zero-flux boundary conditions within a smooth, bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> (with <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>). The parameters involved are <span><math><mi>χ</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>r</mi><mo>≥</mo><mn>0</mn></math></span>, and <span><math><mi>η</mi><mo>&gt;</mo><mn>0</mn></math></span>. It is demonstrated that, provided <span><math><mi>γ</mi><mo>&gt;</mo><mn>3</mn><mo>−</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>N</mi></mrow></mfrac></math></span>, for sufficiently smooth initial data, the corresponding initial-boundary problem admits a unique global-in-time classical solution, which remains uniformly bounded. To the best of our knowledge, these are the first results concerning the boundedness of solutions for this parabolic-elliptic-ODE system in higher dimensions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129473"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600799","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":"Large time behavior of a quasilinear two-species attraction-repulsion chemotaxis system with two chemicals","authors":"Miaoqing Tian ,&nbsp;Fuxin Yu ,&nbsp;Xinchun Gao ,&nbsp;Jiahui Hu","doi":"10.1016/j.jmaa.2025.129471","DOIUrl":"10.1016/j.jmaa.2025.129471","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with the quasilinear two-species attraction-repulsion chemotaxis system with two chemicals: &lt;span&gt;&lt;math&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;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&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;mo&gt;−&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&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;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&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;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&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;/msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, subject to the homogeneous Neumann boundary conditions in a bounded domain &lt;span&gt;&lt;math&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;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;(&lt;span&gt;&lt;math&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;) with smooth boundary, where the parameters &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Φ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;msup&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;msub&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129471"},"PeriodicalIF":1.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636616","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}