. 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). ...

In this article, the author studies the properties of discrete approximations for mathematical models of coupled thermoelasticity in the stress-temperature formulation. Since many applied problems deal with steep gradients of thermal fields, the main emphasis is given to the investigation of non-smooth solutions of non-stationary thermoelasticity. Convergence of operator-difference schemes on weak solutions of thermoelasticity is proved, and the dispersion analysis of models is performed. Error estimates and the results of computational experiments are presented. Key words: hyperbolic-parabolic models, operator-difference schemes for thermoelasticity problems, weak solutions, optimal error control. 1 Mixed Modes in Dynamics Described by Mathematical Models of Coupled Field Theory. In essence, any mathematical model describes a transformation of different types of energy. The recognition of this fact leads to an integral reformulation of differential models. On the one hand, such a r...