On the damped nonlinear evolution equation \(w_{tt}=\sigma(w)_{xx}- \gamma w_ t\) (Q797055)

This paper is devoted to the study of initial-boundary value problems for the damped \((\gamma>0)\) quasi-linear wave equation \(w_{tt}=\sigma(w)_{xx}-\gamma w_ t\) when \(\sigma '(0)=0\) or when \(\sigma '(0)>0\) but \(\sigma '(r)<0\) for \(| r|\) sufficiently large. In addition to global non-existence theorems for sufficiently smooth solutions, the author also obtains various growth estimates which are valid on the maximal interval of existence.