We consider the global existence of strong solution , corresponding to a class of fully nonlinear wave equations with strongly damped terms in a bounded and smooth domain in , where is a given monotone in nonlinearity satisfying some dissipativity and growth restrictions and is in a sense subordinated to . By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution .
Zhigang Pan. Hong Luo. Tian Ma. "Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/805158