On the asymptotic properties of a class of nonlinear parabolic equations

Abstract

We consider a class of nonlinear parabolic equations which may be thought of as a generalisation of the classical heat equation, where the coefficient of thermal conductivity depends appreciably on the temperature.

We show that, under certain restrictions on the nonlinearity involved, the value of the solution approaches the value of a corresponding linearised equation asymptotically.

Physically this means that in the case that the coefficient of thermal conductivity varies, the asymptotic behaviour of the temperature profile is governed, essentially, by the value of that coefficient at the temperature of the surrounding medium.

Additional information

Notes on contributors

J. P. G. Ewer

Wolfgang Walter