## Diffusion in Poro-Elastic Media (1998)

Venue: | Jour. Math. Anal. Appl |

Citations: | 10 - 7 self |

### BibTeX

@ARTICLE{Showalter98diffusionin,

author = {R. E. Showalter},

title = {Diffusion in Poro-Elastic Media},

journal = {Jour. Math. Anal. Appl},

year = {1998},

volume = {251},

pages = {200--0}

}

### OpenURL

### Abstract

. Existence, uniqueness and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasi-static assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...