Large time behavior of solutions of a dissipative semilinear heat equation

Journal Article · Sun Dec 31 04:00:00 EST 1995 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309508821138· OSTI ID:161665

Escobedo, M ^[1]; Kavian, O ^[2]; Matano, Hiroshi ^[3]

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1. Universidad del Pais Vasco, Bilbao (Spain)
2. Universite de Versailles (France)
3. Univ. of Tokyo (Japan)

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.

• Sponsoring Organization: USDOE
• OSTI ID: 161665
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 7-8 Vol. 20; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ANALYTICAL SOLUTION
DIFFUSION
FOURIER HEAT EQUATION
NONLINEAR PROBLEMS
VARIATIONAL METHODS