Journal of Mathematical Analysis and Applications最新文献_第2页

A structure-preserving reduced-order finite difference approach for a class of semilinear stochastic partial differential equations driven by white noise 一类由白噪声驱动的半线性随机偏微分方程的保结构降阶有限差分方法

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-17 DOI: 10.1016/j.jmaa.2025.129807

Jiangping Dong , Wei Zhao , Huanrong Li

{"title":"A structure-preserving reduced-order finite difference approach for a class of semilinear stochastic partial differential equations driven by white noise","authors":"Jiangping Dong , Wei Zhao , Huanrong Li","doi":"10.1016/j.jmaa.2025.129807","DOIUrl":"10.1016/j.jmaa.2025.129807","url":null,"abstract":"<div><div>This paper presents a novel reduced-order finite difference (ROFD) approach that integrates proper orthogonal decomposition (POD) with the finite difference (FD) method to efficiently solve a class of semilinear stochastic partial differential equations (SPDEs) driven by white noise. SPDEs are a class of mathematical models that incorporate random terms or stochastic processes to describe the evolution of systems under uncertainty. SPDEs play a crucial role in modeling real-world phenomena across various fields, including physics, finance, and environmental science, where stochastic process is an inherent component. However, the presence of noise terms and selection of large sample data pose significant challenges for numerical solutions. The proposed ROFD method not only retains the approximation accuracy of the original FD method but also preserves the structural properties of the original semilinear SPDEs. For instance, the mathematical expectation of the numerical solutions under large-sample data satisfies the maximum principle, energy dissipation and so on. A series of numerical experiments have been performed to evaluate the effectiveness of the ROFD method in solving a class of semilinear SPDEs. The numerical results demonstrate that the ROFD method provides highly accurate numerical solutions, exhibits excellent stability and significantly enhances computational efficiency. Due to these advantages, it serves as a highly competitive and practical numerical method for addressing complex SPDEs in real-world applications.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129807"},"PeriodicalIF":1.2,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322875","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}

引用次数: 0

A lowest-order divergence-free virtual element method for Navier-Stokes equations with damping on polygonal mesh 多边形网格上具有阻尼的Navier-Stokes方程的一种低阶无散度虚元法

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129792

Yanping Chen , Qing Li , Jian Huang , Yu Xiong

引用次数: 0

Symmetry of finite energy solutions to critical p-Laplacian systems in RN RN中临界p-拉普拉斯系统有限能量解的对称性

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129812

Min Zhou, Zexin Zhang

引用次数: 0

Fundamental solutions for parabolic equations and systems: Universal existence, uniqueness, representation 抛物方程和系统的基本解：普遍存在，唯一性，表示

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129806

Pascal Auscher, Khalid Baadi

{"title":"Fundamental solutions for parabolic equations and systems: Universal existence, uniqueness, representation","authors":"Pascal Auscher, Khalid Baadi","doi":"10.1016/j.jmaa.2025.129806","DOIUrl":"10.1016/j.jmaa.2025.129806","url":null,"abstract":"<div><div>In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smooth, time-dependent, elliptic part having a variational definition. Our classes of weak solutions are taken with minimal assumptions. We prove the existence and uniqueness of a fundamental solution which seems new in this generality: it is shown to always coincide with the associated evolution family for the initial value problem with zero source and it yields representation of all weak solutions. Our strategy is a variational approach avoiding density arguments, a priori regularity of weak solutions or regularization by smooth operators. One of our main tools are embedding results which yield time continuity of our weak solutions going beyond the celebrated Lions regularity theorem and that is addressing a variety of source terms. We illustrate our results with three concrete applications: second order uniformly elliptic part with Dirichlet boundary condition on domains, integro-differential elliptic part, and second order degenerate elliptic part.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 1","pages":"Article 129806"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144321438","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}

引用次数: 0

Automorphisms of subalgebras of bounded analytic functions 有界解析函数的子代数的自同构

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129804

Kanha Behera, Rahul Maurya, P. Muthukumar

{"title":"Automorphisms of subalgebras of bounded analytic functions","authors":"Kanha Behera, Rahul Maurya, P. Muthukumar","doi":"10.1016/j.jmaa.2025.129804","DOIUrl":"10.1016/j.jmaa.2025.129804","url":null,"abstract":"<div><div>Let <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> denote the algebra of all bounded analytic functions on the unit disk. It is well-known that every (algebra) automorphism of <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> is a composition operator induced by disc automorphism. Maurya et al., (J. Math. Anal. Appl. 530: Paper No: 127698, 2024) proved that every automorphism of the subalgebras <span><math><mo>{</mo><mi>f</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>:</mo><mi>f</mi><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn><mo>}</mo></math></span> or <span><math><mo>{</mo><mi>f</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>:</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mn>0</mn><mo>)</mo><mo>=</mo><mn>0</mn><mo>}</mo></math></span> is a composition operator induced by a rotation. In this article, we give very simple proof of their results. As an interesting generalization, for any <span><math><mi>ψ</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>, we show that every automorphism of <span><math><mi>ψ</mi><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> must be a composition operator and characterize all such composition operators. Using this characterization, we find all automorphism of <span><math><mi>ψ</mi><msup><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> for few choices of <em>ψ</em> with various nature depending on its zeros.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"552 2","pages":"Article 129804"},"PeriodicalIF":1.2,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144322873","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}

引用次数: 0

Maximum principles and consequences for γ-translators in Rn+1 II Rn+1中γ-翻译器的最大原理和后果

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129809

José Torres Santaella

引用次数: 0

On the algebraic lower bound for the radius of spatial analyticity for the Zakharov-Kuznetsov and modified Zakharov-Kuznetsov equations 关于Zakharov-Kuznetsov方程和修正Zakharov-Kuznetsov方程空间解析半径的代数下界

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129802

Mikaela Baldasso, Mahendra Panthee

引用次数: 0

Local and global bifurcation analysis of density-suppressed motility model 密度抑制运动模型的局部和全局分岔分析

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129810

Di Liu , Junping Shi , Weihua Jiang

引用次数: 0

Infinite divisibility of the product of two correlated normal random variables and exact distribution of the sample mean 两个相关的正态随机变量乘积的无限可整除性和样本均值的精确分布

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129800

Robert E. Gaunt , Saralees Nadarajah , Tibor K. Pogány

引用次数: 0

Fractal representations of the number zero on the parabola curve 分形表示抛物线曲线上的数字零

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-06-16 DOI: 10.1016/j.jmaa.2025.129801

Xuemin Wang , Yi Lu , Jingjing Chen , Kan Jiang

引用次数: 0