Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation (Journal of Partial Differential Equations, 2003)
" In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equation u_{tt} + k_1u_{xxxx} + k_2u_{xxxxt} + g(u_{xx})_{xx} = f(x, t) are proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given."
Keywords: Nonlinear hyperbolic equation; initial boundary value problem; global solution; blow-up of solution