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.
翻译:在本文中,我们研究了非线性孔径弹性模型的薄弱溶液的存在和独特性。为了更好地描述原始模型的变形和扩散过程,我们首先通过多物理学方法重新配置非线性孔径弹性。然后,我们采用了类似的技术来证明非线性孔径孔径模型的精度,以证明非线性孔径弹性模型的薄弱溶液的存在和独特性。我们严格地证明非线性应力-压力紧张关系的增长、共生性和单一性,提供能源估计,并利用Schauder的固定点定点来显示非线性孔径孔径模型的薄弱溶液的存在和独特性。