随机机电双域模型 *

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-06-07 DOI:10.1088/1361-6544/ad5132
M Bendahmane, K H Karlsen, F Mroué
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引用次数: 0

摘要

我们分析了一个椭圆-解析混合型非线性随机偏微分方程(SPDE)系统,该系统模拟电信号的传播及其对心脏组织变形的影响。该系统控制离子量、细胞内外电位和线性化弹性方程的动态。我们引入了一个称为主动应变分解的框架,它将变形的材料梯度分为主动(依赖电生理学)部分和弹性(被动)部分,以捕捉肌肉收缩、生化反应和电活动之间的耦合。在线性化弹性行为和非线性扩散截断的假设下,我们提出了随机机电双域模型,并建立了该模型的弱解存在性。为了通过近似解的收敛性来证明存在性,我们采用了随机紧凑性方法、辅助非退化系统和 Faedo-Galerkin 方法。我们利用德拉姆定理的随机调整来推导压力近似的弱收敛性。
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Stochastic electromechanical bidomain model *
We analyse a system of nonlinear stochastic partial differential equations (SPDEs) of mixed elliptic-parabolic type that models the propagation of electric signals and their effect on the deformation of cardiac tissue. The system governs the dynamics of ionic quantities, intra and extra-cellular potentials, and linearised elasticity equations. We introduce a framework called the active strain decomposition, which factors the material gradient of deformation into an active (electrophysiology-dependent) part and an elastic (passive) part, to capture the coupling between muscle contraction, biochemical reactions, and electric activity. Under the assumption of linearised elastic behaviour and a truncation of the nonlinear diffusivities, we propose a stochastic electromechanical bidomain model, and establish the existence of weak solutions for this model. To prove existence through the convergence of approximate solutions, we employ a stochastic compactness method in tandem with an auxiliary non-degenerate system and the Faedo–Galerkin method. We utilise a stochastic adaptation of de Rham’s theorem to deduce the weak convergence of the pressure approximations.
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来源期刊
Nonlinearity
Nonlinearity 物理-物理:数学物理
CiteScore
3.00
自引率
5.90%
发文量
170
审稿时长
12 months
期刊介绍: Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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