Existence of global smooth solutions to the initial-boundary value problem for the quasi-linear wave equation with a degenerate dissipative term (Q1196641)

The initial-boundary value problem for the quasi-linear, dissipative wave equation \[ u_{tt}-\nabla(\sigma(|\nabla u|^ 2)\nabla u)+a(x)u_ t=0 \] is discussed under hypotheses which require \(a\) to be a non-negative (not necessarily bounded below by a positive constant as in previous work) provided its reciprocal is \(p\)th power integrable, \(0<p<1\). The main result is the global existence of smooth solutions with small initial data.