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

Abstract

We consider the global existence of strong solutionu, corresponding to a class of fully nonlinear wave equations with strongly damped termsutt-kΔut=f(x,Δu)+g(x,u,Du,D2u)in a bounded and smooth domainΩinRn, wheref(x,Δu)is a given monotone inΔunonlinearity satisfying some dissipativity and growth restrictions andg(x,u,Du,D2u)is in a sense subordinated tof(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solutionu∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

Structural stability analysis of solutions to the initial boundary value problem for a nonlinear strongly damped wave equation

“…Different conclusions were obtained in many other articles [2,7,10,13,15,16]. References [1,[3][4][5]12] can be given for more information on the structural stability result for interested readers.…”

Existence-uniqueness of strong solution to a class of quasi-linear damped wave equations with gradient term

“…When f satisfying some weak growth restrictions, we obtained the global existence and uniqueness of strong solution u ∈ C 0 ((0, ∞), H 2 (Ω)). In [16], we have discussed a class of fully nonlinear wave equations with strongly damped terms in a bounded and smooth domain in R n , where f (x, u) is a given monotone in u nonlinearity satisfying some dissipativity and growth restrictions and g(x, u, Du, D 2 u) is in a sense subordinated to f (x, u). It is pity that we didn't obtain the uniqueness of strong solution.…”