No abstract

Existence, uniqueness, and regularity theory is developed for a general initialboundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static 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. ᮊ

As a final example of the physical origin of (1.1) we mention the theory of seepage of homogeneous fluids through a fissured rock [4]. A fissured rock consists of blocks of porous and permeable material separated by fissures or "cracks." The liquid then flows through the blocks and also between the blocks through the fissures. In this context an analysis of the pressure in the fissures leads to (1.1), where r/represents a characteristic of the fissured rock. A decrease in q corresponds to a reduction in block dimensions and an increase in the degree of fissuring, and (1.1) then tends to coincide with the classical parabolic equation (1.2) of seepage of a liquid under elastic conditions. The equation which we shall consider here is an example of the general class of equations of Sobolev type, sometimes referred to as the Sobolev-Galpern type. These are characterized by having mixed time and space derivatives appearing in the highest order terms of the equation. Such an equation was studied by Sobolev

The initial-value problem is studied for evolution equations in Hilbert AMS(MOS) 78712.Sponsored by th., I!!The responsibility for the wording and views expressed in this descriptive summary lies with MRC, and not with the authors of this report.