Existence of a weak solution for a quasilinear wave equation with boundary condition

Alain Hertzog; Antoine Mondoloni

doi:10.3934/cpaa.2002.1.191

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2002, Volume 1, Issue 2: 191-219. Doi: 10.3934/cpaa.2002.1.191

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Existence of a weak solution for a quasilinear wave equation with boundary condition

Alain Hertzog^1, and
Antoine Mondoloni^1,

1.
Department of Mathematics, University of Corsica, UMR CNRS 6134 S.P.E., BP 52, 20250 Corte

Received: June 30, 2001

Revised: October 31, 2001

Published: May 2002

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Abstract

In this paper we get by the Glimm scheme the existence of a weak solution to the quasilinear wave equation $w_{t t}=( \sigma_n(w_x))_x$ where $\sigma_n(x)=ax+\gamma x^{2n+1}$, $\alpha$, $ \gamma>0$ and $n$ is an integer $n\ge 1$ with $w_x(0,t)=0$ for initial data not necessarily small.

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Mathematics Subject Classification: Primary 35L65.

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