Global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms
Summary: We consider the global existence of strong solutions for a class of fully nonlinear wave equations with strongly damping terms \(u_{tt} - k\Delta u_t = f(x, \Delta u) + g(x, u, Du, D^2u)\) in a bounded and smooth domain \(\Omega\) in \(\mathbb {R}^n\), where \(f(x, \Delta u)\) is a given monotone in \(\Delta u\) nonlinearity satisfying some dissipativity and growth restrictions, and \(g(x, u, Du, D^2 u)\) is in a sense subordinated to \(f(x, \Delta u)\). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution \(u \in L^\infty_{\text{loc}}((0, \infty), W^{2,p}(\Omega) \cap W^{1,p}_0(\Omega))\).
scientific article; zbMATH DE number 6106315
scientific article