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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

Alain Hertzog 1, and  Antoine Mondoloni 1,

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.
Keywords: bounded variation function., Glimm functional, Riemann invariants, Riemann problem, p-system, Glimm scheme, wave interactions.
Mathematics Subject Classification: Primary 35L6.
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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