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Asymptotics for symmetric hyperbolic systems with a large parameter. (English) Zbl 0685.35014

From author’s abstract: The asymptotic behavior as \(\lambda\) \(\to \infty\) is analysed for solutions u(\(\lambda)\) of quasilinear symmetric hyperbolic systems of the form \[ A^ 0u_ t+A^ ju_{x_ j}+\lambda C^ ju_{x_ j}=F;\quad u(0,x,\lambda)=u_ 0(x,\lambda), \] where the \(A^ k\) and F depend on t,x,u, and u/\(\lambda\), but the \(C^ j\) are constant. The results are applied to the equations of slightly compressible fluid dynamics to obtain a generalized form of the acoustics equations that describe the first-order correction in incompressible flow. The special case of a barotropic fluid was analyzed previously by Klainerman and Majda.
Reviewer: T.C.T.Ting

MSC:

35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35L45 Initial value problems for first-order hyperbolic systems

Keywords:

parameter; acoustics
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References:

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