The heat conduction model involving two temperatures on the segment with Wentzell boundary conditions

Abstract

According to the theory of relatively p-bounded operators, we study the Heat Conduction model involving two temperatures for isotropic material, which describes, the rate of change of internal energy due to the movement of the heat flux form one medium to its complement with general Wentzell boundary conditions. In particular, we consider spectrum of one-dimensional Laplace operator on the segment [0,1] with general Wentzell boundary conditions. We examine the relative spectrum in one-dimensional Heat Conduction equation involving two temperatures, and construct the resolving group in the Cauchy-Wentzell problem with general Wentzell boundary conditions. In the paper, these problems are solved under the assumption that the initial space is a contraction of the space L2(0,1).