. 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). ...

A simple 1D model for crystal dissolution and precipitation is presented. The model equations resemble a one-phase Stefan problem and involve non-linear and multivalued exchange rates at the free boundary. The original equations are formulated on a variable domain. By transforming the model to a fixed domain and applying a regularization, we prove the existence and uniqueness of a solution. The paper is concluded by numerical simulations.

A system of parabolic integro-differential equations arising in the study of thermoelastic contact of two rods is considered. The questions of existence, uniqueness and continuous dependence of the solution upon the data are demonstrated via the theoretical potential solution representation technique and theory of Volterra equations of second kind. An application to linear thermoelasticity is also given. Keywords: Parabolic, integro-differential, non-local, thermoelastic contact. AMS(MOS) subject classification:35K50, 73C25, 73J05. 1. Introduction In this paper we consider the following parabolic system of finding U = (u 1 (x; t); u 2 (x; t)) such that u 1 t \Gamma c 1 u 1 xx = b 1 l 1 d dt maxfI(U); 0g ; in Q 1 T = (0; l 1 ) \Theta J; (1.1) u 2 t \Gamma c 2 u 2 xx = b 2 1 \Gamma l 2 d dt maxfI(U); 0g ; in Q 2 T = (l 2 ; 1) \Theta J; (1.2) u 1 (x; 0) = OE 1 (x); 0 ! x ! l 1 ; (1.3) u 2 (x; 0) = OE 2 (x); l 2 ! x ! 1; (1.4) ¯ 1 u 1 x (0; t) + 1 u 1...