强耦合随机退化反应扩散系统的无效可控性

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-09-26 DOI:10.1016/j.jmaa.2024.128911

Lin Yan , Bin Wu

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引用次数: 0

摘要

本文涉及心脏电生理学中一个强耦合随机退化反应-扩散系统的空可控性，该系统描述了具有随机效应的心脏组织中的电活动。为了解决该系统的退化问题，我们首先考虑该耦合随机退化系统的近似问题。通过加权同一法，我们证明了这个近似问题的邻接系统的统一卡勒曼估计，该系统是一个具有同质诺伊曼边界条件的强耦合后向随机抛物线系统。基于这个卡勒曼估计和一个极限过程，我们最终得到了空可控性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Null controllability for a strongly coupled stochastic degenerate reaction-diffusion system

This paper concerns the null controllability for a strongly coupled stochastic degenerate reaction-diffusion system in cardiac electrocardiology, which describes the electrical activity in the cardiac tissue with random effects. To deal with degeneracy of this system, we first consider an approximate problem of this coupled stochastic degenerate system. By a weighted identity method, we then prove a uniform Carleman estimate for the adjoint system of this approximate problem, which is a strongly coupled backward stochastic parabolic system with homogeneous Neumann boundary conditions. Based on this Carleman estimate and a limit process, we finally obtain the null controllability result.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.