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

• 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.
Mathematics Subject Classification: Primary 35L65.

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