Journal of Mathematical Analysis and Applications最新文献

{"title":"Generalized C⁎-convexity in completely positive maps","authors":"Anand O. R,&nbsp;K. Sumesh","doi":"10.1016/j.jmaa.2025.129700","DOIUrl":"10.1016/j.jmaa.2025.129700","url":null,"abstract":"<div><div>In this paper, we generalize a specific quantized convexity structure of the generalized state space of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra and examine the associated extreme points. We introduce the notion of <em>P</em>-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-convex subsets, where <em>P</em> is any positive operator on a Hilbert space <span><math><mi>H</mi></math></span>. These subsets are defined with in the set of all completely positive (CP) maps from a unital <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra <span><math><mi>A</mi></math></span> into the algebra <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of bounded linear maps on <span><math><mi>H</mi></math></span>. In particular, we focus on certain <em>P</em>-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-convex sets, denoted by <span><math><msup><mrow><mi>CP</mi></mrow><mrow><mo>(</mo><mi>P</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo><mo>)</mo></math></span>, and analyze their extreme points with respect to this new convexity structure. This generalizes the existing notions of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-convex subsets and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points of unital completely positive maps. We significantly extend many of the known results regarding the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points of unital completely positive maps into the context of <em>P</em>-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-convex sets we are considering. This includes an abstract characterization and the structure of <em>P</em>-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points. Further, we discuss the connection between <em>P</em>-<span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points and linear extreme points of these convex sets, as well as Krein-Milman type theorems. Additionally, using these studies, we completely characterize the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-extreme points of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-convex set of all contractive completely positive maps from <span><math><mi>A</mi></math></span> into <span><math><mi>B</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span>, where <span><math><mi>H</mi></math></span> is finite-dimensional.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129700"},"PeriodicalIF":1.2,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134551","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 multiplicity result for Hamiltonian systems with mixed periodic-type and Neumann-type boundary conditions","authors":"Wahid Ullah","doi":"10.1016/j.jmaa.2025.129701","DOIUrl":"10.1016/j.jmaa.2025.129701","url":null,"abstract":"<div><div>We study the multiplicity of solutions for a Hamiltonian system coupling two systems associated with mixed boundary conditions: corresponding to the first system, we impose periodic boundary conditions and assume the twist condition commonly used for the Poincaré–Birkhoff theorem, while for the second one, we consider a two-point boundary conditions of Neumann type.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129701"},"PeriodicalIF":1.2,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134549","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":"Commuting conjugations for operators being far from unitary operators","authors":"P. Dymek,&nbsp;A. Płaneta,&nbsp;M. Ptak","doi":"10.1016/j.jmaa.2025.129699","DOIUrl":"10.1016/j.jmaa.2025.129699","url":null,"abstract":"<div><div>For a given operator <em>T</em>, we investigate when there exists a conjugation commuting with <em>T</em>. If <em>T</em> is an analytic left-invertible operator (or left-invertible operator with the wandering subspace property), we obtain equivalent conditions for the existence of such a conjugation. We apply our results to the case of weighted shifts with matricial symbols.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129699"},"PeriodicalIF":1.2,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170766","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 non-integrability of the electro-dissolution of copper","authors":"Azad Ibrahim Amen ,&nbsp;Jihan Mustafa Mirkhan","doi":"10.1016/j.jmaa.2025.129696","DOIUrl":"10.1016/j.jmaa.2025.129696","url":null,"abstract":"<div><div>In this work, we investigate integrability of three-dimensional systems for the copper electro-dissolution model, which are expressed as nonlinear ordinary differential equations<span><span><span><math><mover><mrow><mi>X</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mi>Y</mi><mo>,</mo><mover><mrow><mi>Y</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mi>Z</mi><mo>,</mo><mover><mrow><mi>Z</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>=</mo><mo>−</mo><mi>Z</mi><mo>−</mo><mi>μ</mi><mi>X</mi><mo>−</mo><mn>1.3</mn><mi>Y</mi><mo>+</mo><msup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1.425</mn><msup><mrow><mi>Y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>0.2</mn><mi>X</mi><mi>Z</mi><mo>−</mo><mn>0.01</mn><msup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>Z</mi><mo>.</mo></math></span></span></span> Where <span><math><mi>X</mi><mo>,</mo><mi>Y</mi></math></span> and <em>Z</em> represent chemical concentrations, and <em>μ</em> is a real parameter. More precisely, we prove: first that the system has no polynomial, rational and Darboux first integrals and second that the system has no analytic first integrals in a neighborhood at the origin when <span><math><mi>μ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>13</mn></mrow><mrow><mn>10</mn></mrow></mfrac><mo>]</mo></math></span> or <span><math><mi>μ</mi><mo>≠</mo><mfrac><mrow><mo>(</mo><mn>13</mn><mspace></mspace><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>16</mn><mspace></mspace><mi>n</mi><mo>+</mo><mn>13</mn><mo>)</mo><mspace></mspace><mi>n</mi></mrow><mrow><mn>10</mn><mspace></mspace><msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>3</mn></mrow></msup></mrow></mfrac></math></span> where <span><math><mi>n</mi><mo>∈</mo><mi>Z</mi><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span> as well as in a neighborhood at the equilibrium point <span><math><mo>(</mo><mi>μ</mi><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></span> when <span><math><mi>μ</mi><mo>=</mo><mfrac><mrow><mn>370</mn></mrow><mrow><mn>13</mn></mrow></mfrac><mo>±</mo><mfrac><mrow><mn>200</mn><mspace></mspace><msqrt><mrow><mn>3</mn></mrow></msqrt></mrow><mrow><mn>13</mn></mrow></mfrac></math></span> or <span><math><mi>μ</mi><mo>&lt;</mo><mn>0</mn></math></span> and <span><math><mfrac><mrow><mn>13</mn><mspace></mspace><msup><mrow><mo>(</mo><mi>μ</mi><mo>−</mo><mn>10</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mn>1000</mn></mrow></mfrac><mo>+</mo><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129696"},"PeriodicalIF":1.2,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134552","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 Hodge-Laplacian on the Čech-de Rham complex governs coupled problems","authors":"Wietse M. Boon ,&nbsp;Daniel F. Holmen ,&nbsp;Jan M. Nordbotten ,&nbsp;Jon E. Vatne","doi":"10.1016/j.jmaa.2025.129692","DOIUrl":"10.1016/j.jmaa.2025.129692","url":null,"abstract":"<div><div>By endowing the Čech-de Rham complex with a Hilbert space structure, we obtain a Hilbert complex with sufficient properties to allow for well-posed Hodge-Laplace problems. We observe that these Hodge-Laplace equations govern a class of coupled problems arising from physical systems including elastically attached rods, multiple-porosity flow systems and 3D-1D coupled flow models.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129692"},"PeriodicalIF":1.2,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138484","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 revisit on well-posedness of a boundary value problem of a stationary advection equation without the separation condition","authors":"Masaki Imagawa,&nbsp;Daisuke Kawagoe","doi":"10.1016/j.jmaa.2025.129695","DOIUrl":"10.1016/j.jmaa.2025.129695","url":null,"abstract":"<div><div>We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-based function spaces for <span><math><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mo>∞</mo></math></span> under the separation condition of the inflow and the outflow boundaries. In this article, we provide another sufficient condition for the well-posedness with <span><math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129695"},"PeriodicalIF":1.2,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124570","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":"Increasing sequences in ordered Banach spaces – New theorems and open problems","authors":"Jochen Glück","doi":"10.1016/j.jmaa.2025.129694","DOIUrl":"10.1016/j.jmaa.2025.129694","url":null,"abstract":"<div><div>An ordered Banach space <em>X</em> is said to have the Levi property or to be regular if every increasing order bounded net (equivalently, sequence) is norm convergent. We prove four theorems related to this classical concept:</div><div>(i) The Levi property follows from the – formally weaker – assumption that every increasing net that has a minimal upper bound is norm convergent. This motivates a discussion about in which sense the Levi property resembles the notion of order continuous norm from Banach lattice theory.</div><div>(ii) If <em>X</em> is separable and has normal cone, then the assumption that every increasing order bounded sequence has a supremum implies the Levi property. This generalizes a classical result about Banach lattices, but requires new ideas since one cannot work with disjoint sequences in the proof.</div><div>(iii) A version of Dini's theorem for ordered Banach spaces that is more general than what is typically stated in the literature. We use this to derive a sufficient condition for the space of all compact operators between two Banach lattices to have the Levi property.</div><div>(iv) Dini's theorem never holds on reflexive ordered Banach spaces with non-normal cone – i.e., on such a space one can always find an increasing sequence that converges weakly but not in norm.</div><div>We illustrate our results by various examples and counterexamples and pose three open problems.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129694"},"PeriodicalIF":1.2,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170511","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":"Li-Yau estimates and Harnack inequalities for nonlinear slow diffusion equations on a smooth metric measure space","authors":"Ali Taheri,&nbsp;Vahideh Vahidifar","doi":"10.1016/j.jmaa.2025.129691","DOIUrl":"10.1016/j.jmaa.2025.129691","url":null,"abstract":"<div><div>We present new gradient estimates and Harnack inequalities for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><mi>d</mi><mi>μ</mi><mo>)</mo></math></span> with invariant weighted measure <span><math><mi>d</mi><mi>μ</mi><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>d</mi><msub><mrow><mi>v</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> and diffusion operator <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>ϕ</mi></mrow></msup><mrow><mi>div</mi></mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>∇</mi><mo>)</mo></math></span> – the <em>ϕ</em>-Laplacian. The nonlinear slow diffusion equation, then, for <span><math><mi>x</mi><mo>∈</mo><mi>M</mi></math></span> and <span><math><mi>t</mi><mo>&gt;</mo><mn>0</mn></math></span>, and fixed exponent <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span>, takes the form<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>N</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>)</mo><mo>.</mo></math></span></span></span> We assume that the metric tensor <em>g</em> and potential <em>ϕ</em> are both space-time dependent; hence the same is true of the usual metric and potential dependent differential operators and curvature tensors. The estimates are established under natural lower bounds on the Bakry-Émery <em>m</em>-Ricci curvature tensor and the time derivative of metric tensor. The curious interplay between geometry, nonlinearity and evolution and their influence on the estimates is at the centre of this investigation. The results here considerably extend and improve earlier results on slow diffusion equations. Several implication, special cases and corollaries are presented and discussed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129691"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134981","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":"Residually finite partial actions and MF Fell bundles","authors":"Timothy Rainone","doi":"10.1016/j.jmaa.2025.129693","DOIUrl":"10.1016/j.jmaa.2025.129693","url":null,"abstract":"<div><div>We study Blackadar and Kirchberg's matricial field (MF) property and quasidiagonality in cross-sectional <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras constructed from Fell bundles and, in particular, from partial <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-dynamical systems. In doing so we generalize Kerr and Nowak's notion of a residually finite action to partial topological dynamical systems. We look at some examples exhibiting this property including the partial Bernoulli shift which produces an MF reduced crossed product provided the group in question is exact, residually finite, and admits an MF reduced group <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 1","pages":"Article 129693"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144134980","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 for an indirect consumption chemotaxis model with signal-dependent motility","authors":"Chun Wu","doi":"10.1016/j.jmaa.2025.129690","DOIUrl":"10.1016/j.jmaa.2025.129690","url":null,"abstract":"<div><div>In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption<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><mrow><mo>(</mo><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>ϕ</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><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><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><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>w</mi><mo>+</mo><mi>u</mi><mo>,</mo></mtd><mtd><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo><mo>∈</mo><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> under the smooth bounded domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mspace></mspace><mspace></mspace><mo>(</mo><mi>n</mi><mo>≤</mo><mn>3</mn><mo>)</mo></math></span> with homogeneous Neumann boundary conditions, where the nonlinearities <span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo></math></span> and the motility function <em>ϕ</em> satisfy the following condition<span><span><span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>u</mi><mo>+</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>m</mi></mrow></msup><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mtext>and</mtext><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>ϕ</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>)</mo><mspace></mspace><mspace></mspace><mtext>is positive on</mtext><mspace></mspace><mspace></mspace><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>.</mo></math></span></span></span> It has been demonstrated that, for any sufficiently regular initial data, the associated initial-boundary value problem allows for global classical solutions. Moreover, the asymptotic behavior of the solutions is analyzed and studied.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"551 2","pages":"Article 129690"},"PeriodicalIF":1.2,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144106445","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}