Energy decay and blow-up of solution for a Kirchhoff equation with dynamic boundary condition
Department of Mathematics, Henan University of Technology, Lianhua Street, Zhengzhou, 450001, P.R. China
Boundary Value Problems 2013, 2013:166 doi:10.1186/1687-2770-2013-166Published: 12 July 2013
The energy decay and blow-up of a solution for a Kirchhoff equation with dynamic boundary condition are considered. With the help of Nakao’s inequality and a stable set, the energy decay of the solution is given. By the convexity inequality lemma and an unstable set, the sufficient condition of blow-up of the solution with negative and small positive initial energy are obtained, respectively.