Existence of a weak solution for a quasilinear wave equation with boundary condition (Q1848479)

The authors prove the existence of a weak solution to the initial-boundary value problem \(w_{tt}=(\sigma(w_{x}))_{x}, x>0,t>0, w_{x}(0,t)=0\) with the initial data having bounded total variation, where \(\sigma (s)=as+bs^{2n+1}, n\geq 1, a>0,b>0. \) The proof depends on three main ingredients: construction of approximate solutions by the Glimm scheme, interaction estimates and decreasing of an appropriate functional.