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Internal layers in high-dimensional domains

Published online by Cambridge University Press:  14 November 2011

Kunimochi Sakamoto
Kunimochi Sakamoto
Affiliation:
Department of Mathematics, Hiroshima University, 3-1 Kagamiyama-1, Higashi-Hiroshima 739, Japan
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Abstract

For a system of semilinear elliptic partial differential equations with a small parameter, denned on a bounded multi-dimensional smooth domain, we show the existence of solutions with internal layers. The high-dimensionality of the domain gives rise to quite interesting an outlook in the analysis, dramatically different from that in one-dimensional settings. Our analysis indicates, in a certain situation, an occurrence of an infinite series of bifurcation phenomena accumulating as the small parameter goes to zero. We also present a related free boundary problem with a possible approach to its resolution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 359 - 401
Copyright
Copyright © Royal Society of Edinburgh 1998

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