Global well-posedness theory for a class of coupled parabolic-elliptic systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Malysheva, Tetyana¹  White, Luther W.² 

[1] Univ Wisconsin, Dept Math & Stat, 2420 Nicolet Dr, Green Bay, WI 54311 USA

[2] Oregon Appl Math Inst, 2130 Ridgeway Dr, Eugene, OR 97401 USA

关键词: Coupled partial differential equations;    Coupled parabolic-elliptic systems;    Well-posedness;    Coupled diffusion-deformation systems;    Thermo-chemo-poroelasticity;   

DOI  :  10.1016/j.jmaa.2020.123923

来源: Elsevier

【 摘 要 】

We consider a fully coupled system consisting of a parabolic equation, with boundary and initial conditions, and an abstract elliptic equation in a variational form with time as a parameter. Such systems appear in applications related to the modeling of coupled diffusion and elastic deformation processes in inhomogeneous porous media within a quasi-static assumption. We establish the global existence, uniqueness, and continuous dependence on initial and boundary data of a weak solution to the system. The proof of this result involves the proposed pseudo-decoupling method which reduces the coupled system to an initial-boundary value problem for a single implicit equation and a refined approach to deriving a priori energy estimates based on component-wise contributions of system parameters to energy norms. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free