David Natroshvili, Levan Giorgashvili, and Shota Zazashvili
abstract:
The purpose of this paper is to construct explicitly, in terms of elementary
functions, fundamental matrices of solutions to the differential equations of
the elasticity theory of hemitropic materials with regard to thermal stresses.
We consider the differential equations corresponding to the static equilibrium
case, and also to the pseudo-oscillations and steady state oscillations cases.
We derive the corresponding Green's formulas and construct the integral
representation formulas of solutions by means of generalized layer and Newtonian
potentials. We formulate the basic boundary value problems in appropriate
function spaces and prove the uniqueness theorems. We develop the potential
method and prove the existence and regularity theorems for basic and mixed type
boundary value problems.
Mathematics Subject Classification: 35J55, 74A60, 74G05, 74G30, 74F05
Key words and phrases: Thermoelasticity theory, elastic hemitropic materials, fundamental matrix, uniqueness theorems, boundary value problems