Qualitative analysis of a nonlinear wave equation (Q1433454)

The author studies the boundary-initial value problem to the equation \[ u_{tt}-a\triangle u+bu_t| u_t| ^{p}=cu| u| ^{q},\quad x\in \Omega \subset \mathbb R^n,\;t>0, \] where \(a,b,c,p,q\) are positive constants, \(p\geq q.\) He proves that a solution of the problem in an unstable set is global but not uniformly bounded and characterizes all bounded global solutions. Moreover, necessary and sufficient conditions for convergence of bounded solutions as \(t\rightarrow \infty \) are given.