TY - JOUR
T1 - Initial Boundary Value Problem for a Damped Nonlinear Hyperbolic Equation
AU - Guowang Chen 
JO - Journal of Partial Differential Equations
VL - 1
SP - 49
EP - 61
PY - 2003
DA - 2003/02
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5405.html
KW - Nonlinear hyperbolic equation
KW - initial boundary value problem
KW - global solution
KW - blow-up of solution
AB -  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.