Existence of Global and Bounded Solutions for Damped Sublinear Wave Equations

We study the initial-boundary value problem for the sublinear wave equations with a linear dampping : u" - △u - ω△u' + δu' = γlulp-2u with the homogeneous Dirichlet boundary condition and H10(Ω) x L2(Ω)-data condition under ω ≥ 0 and δ > -ωλ1. When 1<p<2, we show that the (local) weak solutions are global and uniformly bounded in time t≥0.