Asymptotic behaviour for a partially diffusive relaxation system

Authors:
Miguel Escobedo and Philippe Laurençot

Journal:
Quart. Appl. Math. **61** (2003), 495-512

MSC:
Primary 35K55; Secondary 35B40, 35L60

DOI:
https://doi.org/10.1090/qam/1999834

MathSciNet review:
MR1999834

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Abstract: The time asymptotics of nonnegative and integrable solutions to a partially diffusive relaxation system is investigated. Under suitable assumptions on the relaxation term, the convergence to a self-similar source type solution, either of the heat equation or of the viscous Burgers equation, is proved. The proof relies on optimal decay rates and classical scaling arguments.

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DOI:
https://doi.org/10.1090/qam/1999834

Article copyright:
© Copyright 2003
American Mathematical Society