A damped elastodynamics system under the global injectivity condition: local wellposedness in $$L^p$$-spaces

IF 1.1 4区 数学 Q2 MATHEMATICS, APPLIED
Sébastien Court
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引用次数: 0

Abstract

Abstract The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the elastodynamics equations dealing with the displacement field as main unknown. These equations are coupled with a pressure whose variations characterize the heart beat. This pressure variable corresponds to a Lagrange multiplier associated with the so-called global injectivity condition. We derive the corresponding coupled system with nonhomogeneous boundary conditions where the pressure variable appears. For mathematical convenience a damping term is added, and for a given class of strain energies we prove the existence of local-in-time solutions in the context of the $$L^p$$ L p -parabolic maximal regularity.

Abstract Image

全局注入条件下的阻尼弹性动力学系统:$$L^p$$ -空间中的局部适定性
摘要本文的目的是对心脏组织的力学方面进行数学建模。后者构成了一个总积保持恒定的弹性域。采用以位移场为主要未知量的弹性动力学方程来模拟心脏组织的时间变形。这些方程式与压力相结合,压力的变化是心跳的特征。这个压力变量对应于与所谓的全局注入条件相关的拉格朗日乘数。导出了具有压力变量的非齐次边界条件下的耦合系统。为了数学上的方便,我们增加了一个阻尼项,并且对于给定的应变能,我们证明了在$$L^p$$ L p -抛物极大正则性条件下局部解的存在性。
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来源期刊
CiteScore
1.70
自引率
8.30%
发文量
75
审稿时长
>12 weeks
期刊介绍: Nonlinear Differential Equations and Applications (NoDEA) provides a forum for research contributions on nonlinear differential equations motivated by application to applied sciences. The research areas of interest for NoDEA include, but are not limited to: deterministic and stochastic ordinary and partial differential equations, finite and infinite-dimensional dynamical systems, qualitative analysis of solutions, variational, topological and viscosity methods, mathematical control theory, complex dynamics and pattern formation, approximation and numerical aspects.
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