Well-posedness of weak solution for a nonlinear poroelasticity model

TL;DR

This paper establishes the existence and uniqueness of weak solutions for a nonlinear poroelasticity model by reformulating it through a multiphysics approach and applying fixed point theorems.

Contribution

It introduces a novel reformulation of nonlinear poroelasticity using a multiphysics approach and proves well-posedness with rigorous mathematical techniques.

Findings

Proves growth, coercivity, and monotonicity of nonlinear stress-strain relation.

Provides energy estimates for the nonlinear model.

Uses Schauder's fixed point theorem to establish solution existence and uniqueness.

Abstract

In this paper, we study the existence and uniqueness of weak solution of a nonlinear poroelasticity model. To better describe the proccess of deformation and diffusion underlying in the original model, we firstly reformulate the nonlinear poroelasticity by a multiphysics approach. Then, we adopt the similar technique of proving the well-posedness of nonlinear Stokes equations to prove the existence and uniqueness of weak solution of a nonlinear poroelasticity model. And we strictly prove the growth, coercivity and monotonicity of the nonlinear stress-strain relation, give the energy estimates and use Schauder's fixed point theorem to show the existence and uniqueness of weak solution of the nonlinear poroelasticity model.