Existence of global solutions to some nonlinear dissipative wave equations (Q1900628)

Let \(\Omega\) be a smooth bounded domain. We prove existence of global solutions, i.e., solutions defined for all \(t\in \mathbb{R}\), for dissipative wave equations of the form \(u''- \Delta u+ |u'|^{p- 1} u'= 0\) in \(\Omega\times (- \infty, \infty)\), \(p> 1\), with Dirichlet boundary conditions. When \(\Omega\) is unbounded the same existence result holds for \(p\geq 2\).