Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 529869, 18 pages
Research Article

Hopf Bifurcation with the Spatial Average of an Activator in a Radially Symmetric Free Boundary Problem

Department of Mathematics, Kyonggi University, Suwon 443-760, Republic of Korea

Received 5 August 2010; Accepted 21 October 2010

Academic Editor: Oded Gottlieb

Copyright © 2010 YoonMee Ham. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An interface problem derived by a bistable reaction-diffusion system with the spatial average of an activator is studied on an 𝑛 -dimensional ball. We analyze the existence of the radially symmetric solutions and the occurrence of Hopf bifurcation as a parameter varies in two and three-dimensional spaces.