Thermal waves in absorbing media

Abstract

We discuss the existence of travelling-wave solutions with interfaces for the nonlinear heat equation with absorption ut = a(um)xx – bu(n) with a, b> 0 and m, n Є R. Several situations occur depending on the relative strength of the diffusion and absorption terms reflected by their exponents m and n. We characterize the existence of finite travelling waves in terms of m and n, show their uniqueness up to translations in space and time, and derive their velocity from the wave profile near the interface or front.