Nonstationary Initial Boundary Value Contact Problems of Generalized Elastothermodiffusion

Abstract

The initial boundary value problems with mixed bound- ary conditions are considered for a system of partial dierential equa- tions of generalized electrothermodiusion. Approximate solutions are constructed and a mathematical substantiation of the method is given. It is well known that a wide range of problems of mathematical physics includes boundary value and initial boundary value problems for dieren- tial equations. Such problems are rather dicult to solve because of an enormous variety of geometrical forms of the investigated objects and the complexity of boundary conditions. Hence an important and timely task has arisen to develop suciently eective methods and tools for solving the above-mentioned problems and obtaining their numerical solutions. Until recently no methods were known for solving problems of elasticity by means of conjugate Þelds. However, in the past few years there have appeared and keep on appearing numerous published works dedicated to this topic. The results of our studies in this direction are presented mainly in (1, 2, 3). In this paper, using the generalized Green-Lindsay theory of elastother- modiusion as an example, the approaches to the solution of nonstationary initial boundary value contact problems with mixed boundary conditions are described for a system of partial dierential equations of this theory in a nonhomogeneous medium. These approaches are based on the method of discrete singularities known as the Riesz-Fischer-Kupradze method. The particular case is treated in (4).