Multiple stable patterns in a balanced bistable equation with heterogeneous environments

Abstract

In this article, we present a simple approach to show the existence of nontrivial stable stationary solutions to a balanced bistable reaction–diffusion equation with heterogeneous environments.

Keywords:

• stable pattern
• bistable nonlinearity
• heterogeneous environments

AMS Subject Classifications::

• Primary 35J65
• 35B05
• 58E05
• Secondary 92C15

Acknowledgements

Kazuhiro Kurata was supported in part by Grant-in-Aid for Scientific Research (C) (No. 18540191) from Japan Society for Promotion of Science and Hiroshi Matsuzawa was supported in part by Grant-in-Aid for Young Scientists (B) (No. 20740098) from Japan Society for Promotion of Science. The authors are thankful to the referees for their careful readings and valuable comments for improving the manuscript.