Kinetic approach to the asymptotic behaviour of the solution to diffusion equations
By classical arguments of kinetic theory of rarefied gases, it is proved that the fundamental solution to the heat equation gives the asymptotic representation of the solution of the Cauchy problem for the same equation. Explicit constants for the decay in relative entropy are found. The method i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sapienza Università Editrice
1996-05-01
|
| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1996(2)/329-346.pdf |
| Summary: | By classical arguments of kinetic theory of rarefied gases, it is proved
that the fundamental solution to the heat equation gives the asymptotic representation
of the solution of the Cauchy problem for the same equation. Explicit constants for the
decay in relative entropy are found. The method is subsequently applied to study the
asymptotic behaviour of the solution to a class of uniformly parabolic equations.
|
|---|---|
| ISSN: | 1120-7183 2532-3350 |