Journal of Mathematical Analysis and Applications最新文献

{"title":"Stability of viscous shock profile for convective porous-media flow with degenerate viscosity","authors":"Yechi Liu","doi":"10.1016/j.jmaa.2025.129302","DOIUrl":"10.1016/j.jmaa.2025.129302","url":null,"abstract":"<div><div>In this paper, we are concerned with the large time behavior of viscous shock wave for the convective porous-media equation with degenerate viscosity. We get the regularity of the solution for general initial data and prove the shock wave is nonlinearly stable providing the initial perturbation is small. Moreover, the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> decay rate is obtained, which generalized the famous result <span><span>[18]</span></span>. Note that the traditional energy method and continuity argument can not be directly used for the case discussed in this paper since the degeneration of viscosity. One need to fully utilize the sign of perturbation and its derivative, decompose the integral domain into several parts to ensure that in each part the sign is invariant. Then the stability and the decay rate are obtained by energy method and an area inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129302"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161995","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 Strichartz estimate for many body Schrödinger equations in the waveguide setting","authors":"Ziyue Lyu ,&nbsp;Zehua Zhao","doi":"10.1016/j.jmaa.2025.129310","DOIUrl":"10.1016/j.jmaa.2025.129310","url":null,"abstract":"<div><div>In this short paper, we prove Strichartz estimates for N-body Schrödinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>×</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> where <span><math><mi>m</mi><mo>≥</mo><mn>3</mn></math></span>), provided that interaction potentials are small enough (depending on the number of the particles and the universal constants, not on the initial data). The proof combines both the ideas of Tzvetkov-Visciglia <span><span>[30]</span></span> and Hong <span><span>[17]</span></span>. As an immediate application, the scattering asymptotics for this model is also obtained. This result extends Hong <span><span>[17]</span></span> to the waveguide case.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129310"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161996","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":"Characterizations of BMO with Hausdorff content","authors":"Chenglong Fang ,&nbsp;Liguang Liu ,&nbsp;Yuying Zhang","doi":"10.1016/j.jmaa.2025.129308","DOIUrl":"10.1016/j.jmaa.2025.129308","url":null,"abstract":"<div><div>Let <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>δ</mi></mrow></msubsup></math></span> be the Hausdorff content on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> of order <span><math><mi>δ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>n</mi><mo>]</mo></math></span>. For the space <span><math><mrow><mi>BMO</mi></mrow><mo>(</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>)</mo></math></span> of bounded mean oscillation that is defined with respect to <span><math><msubsup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>δ</mi></mrow></msubsup></math></span>, the authors establish its equivalent characterizations via replacing the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>)</mo></math></span>-integrability in its definition by the Luxemburg type <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo>(</mo><msubsup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>)</mo></math></span>-integrability, where <em>φ</em> can be either a convex or a concave nonnegative function. Typical examples of <em>φ</em> include <span><math><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>, <span><math><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>p</mi><mi>t</mi></mrow></msup><mo>−</mo><mn>1</mn></math></span> and <span><math><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>log</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>⁡</mo><mo>∘</mo><mo>⋯</mo><mo>∘</mo><msub><mrow><mi>log</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>⁡</mo><mi>t</mi></math></span>, where <span><math><mi>p</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>log</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>⁡</mo><mi>t</mi><mo>:</mo><mo>=</mo><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>log</mi><mo>⁡</mo><mi>t</mi><mo>,</mo><mspace></mspace><mn>0</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129308"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143162112","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":"Dulac functions and monodromic singularities","authors":"Isaac A. García ,&nbsp;Jaume Giné ,&nbsp;Ana Livia Rodero","doi":"10.1016/j.jmaa.2025.129309","DOIUrl":"10.1016/j.jmaa.2025.129309","url":null,"abstract":"<div><div>We are interested in bound the maximum number of small amplitude limit cycles that an analytic planar vector field can have bifurcating from any monodromic singularity as well as its stability and hyperbolic nature. We do not use the Poincaré map approach to this problem. Instead, we propose an algorithmic procedure to construct, under some assumptions, a Dulac function in a neighborhood (may be punctured) of the singularity. This approach is based on the existence of a real analytic invariant curve passing through the singularity which allows us to overcome the usual difficulty seeking for the candidates to be a Dulac function. We finally apply our results to a degenerate polynomial monodromic family.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129309"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143161331","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 fixed-point proof of the Darwin vector potential in the Vlasov-Darwin system with generalized variables","authors":"Yaxian Ma,&nbsp;Sen Ming","doi":"10.1016/j.jmaa.2025.129301","DOIUrl":"10.1016/j.jmaa.2025.129301","url":null,"abstract":"<div><div>In this work, we study the well-posedness of the integral equation for the Darwin vector potential in the Vlasov-Darwin system with generalized variables (VDG system). As for this system, local existence, continuation criterion and global existence with small initial data have been established. Due to the effect of the non-relativistic term, a difficulty arises in dealing with the current density. All of the results for the VDG system impose restrictions on the speed of light c. In this work, we overcome this difficulty and use the Schauder fixed point theorem to prove that the integral equation of the Darwin vector potential is well-posed. Furthermore, the well-posedness of the Darwin vector potential does not require any restrictions.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129301"},"PeriodicalIF":1.2,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166886","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 explicit construction of the unitarily invariant quaternionic polynomial spaces on the sphere","authors":"Mozhgan Mohammadpour,&nbsp;Shayne Waldron","doi":"10.1016/j.jmaa.2025.129297","DOIUrl":"10.1016/j.jmaa.2025.129297","url":null,"abstract":"<div><div>The decomposition of the polynomials on the quaternionic unit sphere in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several authors. Typically, these abstract decompositions into “quaternionic spherical harmonics” specify the irreducible representations involved and their multiplicities.</div><div>The elementary constructive approach taken here gives an orthogonal direct sum of irreducibles, which can be described by some low-dimensional subspaces, to which commuting linear operators <em>L</em> and <em>R</em> are applied. These operators map harmonic polynomials to harmonic polynomials, and zonal polynomials to zonal polynomials. We give explicit formulas for the relevant “zonal polynomials” and describe the symmetries, dimensions, and “complexity” of the subspaces involved.</div><div>Possible applications include the construction and analysis of desirable sets of points in quaternionic space, such as equiangular lines, lattices and spherical designs (cubature rules).</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129297"},"PeriodicalIF":1.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166887","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":"Controlled superprocesses and HJB equation in the space of finite measures","authors":"Antonio Ocello","doi":"10.1016/j.jmaa.2025.129298","DOIUrl":"10.1016/j.jmaa.2025.129298","url":null,"abstract":"<div><div>This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are weak scaling limits of controlled branching processes. First, we prove a generalized Itô's formula for this dynamics in the space of finite measures, using the differentiation in the space of finite positive measures. This lays the groundwork for a PDE characterization of the value function of a control problem, which leads to a verification theorem. Finally, focusing on an exponential-type value function, we show how a regular solution to a finite–dimensional HJB equation can be used to construct a smooth solution to the HJB equation in the space of finite measures, via the so-called branching property technique.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129298"},"PeriodicalIF":1.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143131251","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":"The Blaschke–Santaló inequality for the normalized Lp Busemann body","authors":"Xiyu Niu ,&nbsp;Ai-Jun Li ,&nbsp;Qingzhong Huang","doi":"10.1016/j.jmaa.2025.129299","DOIUrl":"10.1016/j.jmaa.2025.129299","url":null,"abstract":"<div><div>The main purpose of this paper is to establish the Blaschke–Santaló inequality for the normalized <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Busemann body. The approach we take is from the functional point of view. By applying the functional <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-Busemann random simplex inequality due to Dann et al. (2016), we establish the Blaschke–Santaló inequality for the functional <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> Busemann body and corresponding moment-entropy inequalities.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129299"},"PeriodicalIF":1.2,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166895","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":"Asymptotic log-Harnack inequality for the 3D stochastic globally modified Allen-Cahn-Navier-Stokes system with degenerate noise","authors":"T. Tachim Medjo","doi":"10.1016/j.jmaa.2025.129293","DOIUrl":"10.1016/j.jmaa.2025.129293","url":null,"abstract":"<div><div>In this article, we consider a globally modified Allen-Cahn-Navier-Stokes equations in a three dimensional bounded domain and examine some asymptotic behaviors of the strong solution. More precisely, we establish the asymptotic log-Harnack inequality for the transition semigroup associated with the globally modified Allen-Cahn-Navier-Stokes system driven by an additive degenerate noise via the asymptotic coupling method. As consequences of the asymptotic log-Harnack inequality, we derive the gradient estimate, the asymptotic irreducibility, the asymptotic strong Feller property, the asymptotic heat kernel estimate and the ergodicity.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129293"},"PeriodicalIF":1.2,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166893","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":"Weighted shifts relevant to CPD matrices and their examples","authors":"George R. Exner ,&nbsp;Il Bong Jung ,&nbsp;Eun Young Lee ,&nbsp;Mi Ryeong Lee","doi":"10.1016/j.jmaa.2025.129295","DOIUrl":"10.1016/j.jmaa.2025.129295","url":null,"abstract":"<div><div>In 1990 R. Curto introduced the notion of <em>n</em>-hyponormality which provides a bridge between subnormal and hyponormal operators. The study of <em>n</em>-hyponormal weighted shifts has been well developed by several mathematicians. In this paper we introduce a property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> for weighted shifts related to <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>×</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> conditionally positive definite matrices, which generalizes <em>n</em>-hyponormality for weighted shifts. First the flatness of a weighted shift with properties <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mn>3</mn><mo>)</mo></math></span> is considered, yielding a result which generalizes previous work. A formula for property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> is constructed, which distinguishes the classes of weighted shifts with property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. We introduce an algorithm to construct weighted shifts with property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and detect the structure related to property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>. Finally, we discuss property <span><math><mi>C</mi><mi>P</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> of a homographic-type weighted shift with a constraint condition.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129295"},"PeriodicalIF":1.2,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166885","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}