TITLE:
On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation
AUTHORS:
Guoguang Lin, Yunlong Gao, Yuting Sun
KEYWORDS:
Nonlinear Higher-Order Kirchhoff Type Equation, Strong Damping, Local Solutions, Blow-Up, Initial Energy
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.6 No.1,
February
13,
2017
ABSTRACT: In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.