Large time behavior of solutions of a dissipative semilnear heat equation

Abstract

In this paper we investigate the large time behavior of solutions of the semilinear heat equation. Where u{sub 0} is the initial data, N {ge} 1 and p > 1. It can be easily checked that if u(t,x) satisfied (1.1), then for {gamma} > 0 the rescaled functions u{sub {gamma}}(t,x) satisfies (1.1), then for {gamma}>0 the rescaled functions define a one parameter family of solutions to (1.1). A solution u {equivalent_to} 0 is said to be self-similar, when u{sub {gamma}} {equivalent_to} u for all {gamma} > 0. For instance, for any fixed p > 1, w{sup *}(t,x):=((p-1)t){sup {minus}1/(p-1)} is such a solution. Actually, it has been proved by H.Brezis, L.A. Peletier & D. Terman that for 1 {infinity}. 15 refs.