On the Fundamental Solution of the Operator of Dynamic Linear Thermodiffusion

Abstract

The fundamental matrix of the 5-by-5 system of partial differential operators describing linear thermodiffusion inside elastic media is – by a standard procedure – expressible through the fundamental solution of its determinant. This determinant is equal to the square of a wave operator multiplied by the so-called operator of dynamic linear thermodiffusion, which is of the fourth order with respect to the time variable. In this paper, we deduce, by means of a variant of Cagniard–de Hoop’s method, a representation of the fundamental solution of this operator by simple definite integrals. This formula allows the explicit computation of thermal and diffusion effects which result from instantaneous point forces or heat sources.