Open Access Research

Energy decay and blow-up of solution for a Kirchhoff equation with dynamic boundary condition

Hongwei Zhang*, Changshun Hou and Qingying Hu

Author Affiliations

Department of Mathematics, Henan University of Technology, Lianhua Street, Zhengzhou, 450001, P.R. China

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Boundary Value Problems 2013, 2013:166  doi:10.1186/1687-2770-2013-166

Published: 12 July 2013

Abstract

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.