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June 1996 Singular Limit of Some Quasilinear Wave Equations with Damping and Restoring Terms
Tokio MATSUYAMA
Tokyo J. Math. 19(1): 197-210 (June 1996). DOI: 10.3836/tjm/1270043229

Abstract

A mixed problem for some hyperbolic equation with small parameter $\varepsilon$ under the presence of a restoring term $|u|^{\alpha}u$ and a reduced problem for a parabolic type are considered. Several $\varepsilon$ weighted energy estimates can be obtained by the method of difference quotients. It is shown that the solution $u_\varepsilon$ of the mixed problem converges, uniformly on any finite time interval, to the solution $u$ of the problem for the parabolic equation in an appropriate Hilbert space as $\varepsilon\to 0$.

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Tokio MATSUYAMA. "Singular Limit of Some Quasilinear Wave Equations with Damping and Restoring Terms." Tokyo J. Math. 19 (1) 197 - 210, June 1996. https://doi.org/10.3836/tjm/1270043229

Information

Published: June 1996
First available in Project Euclid: 31 March 2010

zbMATH: 0861.35007
MathSciNet: MR1391938
Digital Object Identifier: 10.3836/tjm/1270043229

Rights: Copyright © 1996 Publication Committee for the Tokyo Journal of Mathematics

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Vol.19 • No. 1 • June 1996
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