HYPERBOLIC HEAT-CONDUCTION IN THE SEMIINFINITE BODY WITH THE HEAT-SOURCE WHICH CAPACITY LINEARLY DEPENDS ON TEMPERATURE

It is commonly taken for granted that long-time solutions of Cattaneo' s hyperbolic heat conduction equation tend to overlap the related para bolic solutions. Usually, for small times considerable qualitative as well as quantitative differences between the hyperbolic and parabolic solutions are observed which vanish completely for large times. Howeve r, in the case of a heat-conducting body with the temperature dependen t inner heat generation, the quantitative differences may grow with ti me. This arises from the feedback between the temperature and the sour ce capacity. To illustrate this effect; Cattaneo's hyperbolic equation for the semi-infinite body, with the heat source which capacity is li nearly dependent on temperature, is solved analytically by the Laplace transforms method.