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We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,Du,D2u) 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∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms