Bifurcation structure of steady-states forbistable equations with nonlocal constraint

Kousuke Kuto; Tohru Tsujikawa

doi:10.3934/proc.2013.2013.467

Article Contents

2013, Volume 2013: 467-476. Doi: 10.3934/proc.2013.2013.467 open access

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Bifurcation structure of steady-states for bistable equations with nonlocal constraint

Kousuke Kuto^1, and
Tohru Tsujikawa^2,

1.
Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585
2.
Department of Applied Physics, University of Miyazaki, Miyazaki, 889-2192

Received: August 31, 2012

Revised: March 31, 2013

Published: October 2013

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Abstract

This paper studies the 1D Neumann problem of bistable equations with nonlocal constraint. We obtain the global bifurcation structure of solutions by a level set analysis for the associate integral mapping. This structure implies that solutions can form a saddle-node bifurcation curve connecting boundary-layer states with internal-layer states. Furthermore, we exhibit the applications of our result to a couple of shadow systems arising in surface chemistry and physiology.

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Mathematics Subject Classification: Primary: 34B18; Secondary: 34C23, 34E20, 37G10.

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References

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