English

Well-posedness of weak solution for a nonlinear poroelasticity model

Analysis of PDEs 2021-12-24 v1 Numerical Analysis Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2112.12425,
  title  = {Well-posedness of weak solution for a nonlinear poroelasticity model},
  author = {Zhihao Ge and Wenlong He},
  journal= {arXiv preprint arXiv:2112.12425},
  year   = {2021}
}

Comments

20 pages. arXiv admin note: text overlap with arXiv:1411.7464