Asymptotic behaviour for a partially diffusive relaxation system

Escobedo, Miguel; Laurençot, Philippe

doi:10.1090/qam/1999834

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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