Well-posedness of weak solution for a nonlinear poroelasticity model

Zhihao Ge; Wenlong He

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arXiv · 2112.12425

Well-posedness of weak solution for a nonlinear poroelasticity model

Zhihao Ge·Wenlong He

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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.

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Zhihao Ge, Wenlong He. 2021-12-23. Well-posedness of weak solution for a nonlinear poroelasticity model. https://arxiv.org/abs/2112.12425

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