Global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms

We consider the global existence of strong solution u,corresponding to a class of fully nonlinear wave equations with strongly damped terms u tt - kδu t = f(x,δu) + g(x,u,du,d 2u) in a bounded and smooth domain ω in r n,where f(x,δu) is a given monotone in u nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,du,d 2u) is in a sense subordinated to f(x,δu). by using spatial sequence techniques,the galerkin approximation method,and some monotonicity arguments,we obtained the global existence of a solution u ∈ l loc ∞((0,∞),w 2,p(ω) ∩ w 0 1,p(ω)). copyright © 2012 zhigang pan et al.