Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation

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Abstract

A short-time existence theorem is proven for the initial-boundary-value problem for a class of quasilinear symmetric hyperbolic systems containing a constant-coefficient spatial operator multiplied by a large parameter λ. Solutions u are shown to remain bounded independently of λ for a time independent of λ provided that u(0) and ul(0) are bounded independently of λ and certain structural conditions are satisfied. This result is applied to the quasigeostrophic approximation of the shallow water equations and the constant-pressure approximation in combustion, and solutions for these cases are shown to converge to solutions of limiting equations as λ → ∞.

Original languageEnglish
Pages (from-to)400-428
Number of pages29
JournalJournal of Differential Equations
Volume68
Issue number3
DOIs
StatePublished - Jul 1987
Externally publishedYes

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