Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities (Q1884802)

The paper deals with the Cauchy problem to the equation \(u_{tt}-\triangle u+u_t=| u| ^{p-1}u,\) \(t>0,\) \(x\in \mathbb R^n\) (\(n=1,2,3\)), where \(p\in (1+2/n,+\infty)\) for \(n=1,2\) and \(p\in (2,3]\) for \(n=3.\) If the initial data are sufficiently small, then the problem admits a global solution satisfying a decay property.