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Matrix of fundamental solutions for the system of equations of hyperbolic thermoelasticity with two relaxation times and solution of the Cauchy problem. (English) Zbl 0698.73003

Summary: A system of linear partial differential equations describing isotropic, homogeneous temperature-rate-dependent thermoelastic solids has been considered. A matrix of fundamental solutions for the main part of the linear hyperbolic equations system for temperature-rate-dependent thermoelastic solids (the so-called thermoelasticity theory with two relaxation times) has been constructed using the RADON transform. Applying the method of potential theory, we obtained the solution of the Cauchy problem for this system of equations. Basing on the matrix of fundamental solutions for the main part of this equations system and using H rmander’s method we obtained the matrix of fundamental solutions for the entire system of equations of linear three-dimensional hyperbolic thermoelasticity theory.

MSC:

74A15 Thermodynamics in solid mechanics
74F05 Thermal effects in solid mechanics
35A08 Fundamental solutions to PDEs
35L05 Wave equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs

Citations:

Zbl 0698.73004
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