The aim of this paper is to prove some properties of the solution to the Cauchy problem for the system of partial differential equations describing thermoelasticity of nonsimple materials proposed by D. Iesan. Explicit formulas for the Fourier transform and some estimates in Sobolev spaces for the solution of the Cauchy problem are proved.
The aim of this paper is to derive a formula for the solution to the Cauchy problem for the linear system of partial differential equations describing nonsimple thermoelasticity. Some properties of the solution are also presented. It is a first step to study the nonlinear case.
Theories of heat predicting a finite speed of propagation of thermal signals have come into existence during the last 50 years. It is worth emphasizing that in contrast to the classical heat theory, these nonclassical theories involve a hyperbolic type heat equation and are based on experiments exhibiting the actual occurrence of wave-type heat transport (so called second sound). This paper presents a new system of equations describing a nonlocal model of heat propagation with finite speed in the...
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