Global Existence and Asymptotic Stability in Nonlinear Heat Conduction

Abstract

The paper investigates global existence and asymptotic behaviour of classical solutions to an initial-boundary value problem for a system of equations which govern one-dimensional nonlinear heat conduction in solids. Asymptotic stability of equilibrium (steady) solutions is further investigated through a new approach which is based on the wave propagation properties of the model. Finally, some comments are given on a more general, quasi-linear, hyperbolic model for heat conduction in dielectric solids which, besides being compatible with thermodynamics, fits experimental data on second sound speed, heat conductivity, and specific heat.