Three-Scale Singular Limits of Evolutionary PDEs

Bin Cheng, Qiangchang Ju, Steve Schochet*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly bounded for a fixed time as the two parameters tend to zero at different rates. A simple example shows the necessity of those conditions in order for uniform bounds to hold. Under further conditions the solutions of the original system tend to solutions of a limit equation as the parameters tend to zero.

Original languageEnglish
Pages (from-to)601-625
Number of pages25
JournalArchive for Rational Mechanics and Analysis
Volume229
Issue number2
DOIs
StatePublished - 1 Aug 2018

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