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1996 Singular limit of some quasilinear wave equations with damping terms
Tokio Matsuyama
Adv. Differential Equations 1(2): 151-174 (1996).

Abstract

We consider a relation between a mixed problem for a class of quasilinear wave equations with small parameter $\epsilon$ and a reduced problem of a parabolic type. By constructing the stable set the global existence of solutions can be discussed. It is shown that the solution $u_{\epsilon}$ of the mixed problem converges, uniformly on any finite time interval, to the solution $u$ of the parabolic equation in an appropriate Hilbert space as $\epsilon \rightarrow 0$. Several $\epsilon$ weighted energy estimates will be obtained in order to evaluate the difference norm of $u_{\epsilon}-u$

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Tokio Matsuyama. "Singular limit of some quasilinear wave equations with damping terms." Adv. Differential Equations 1 (2) 151 - 174, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0841.35012
MathSciNet: MR1363999

Subjects:
Primary: 35L70
Secondary: 35B25 , 45K05

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 2 • 1996
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