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June  2002, 1(2): 191-219. doi: 10.3934/cpaa.2002.1.191

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

1. 

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

Received  July 2001 Revised  November 2001 Published  March 2002

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.
Citation: Alain Hertzog, Antoine Mondoloni. Existence of a weak solution for a quasilinear wave equation with boundary condition. Communications on Pure & Applied Analysis, 2002, 1 (2) : 191-219. doi: 10.3934/cpaa.2002.1.191
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