On a class of infinite transition solutions for an Allen-Cahn model equation

Paul H. Rabinowitz; Ed Stredulinsky

doi:10.3934/dcds.2008.21.319

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2008, Volume 21, Issue 1: 319-332. Doi: 10.3934/dcds.2008.21.319

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On a class of infinite transition solutions for an Allen-Cahn model equation

Paul H. Rabinowitz^1, and
Ed Stredulinsky^2,

1.
Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706
2.
Department of Mathematics, University of Wisconsin-Rock County, Janesville, WI 53546

Received: February 28, 2007

Revised: May 31, 2007

Published: December 2007

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Abstract

Using minimization arguments and a limit process, we construct a family of solutions which undergo an infinite number of transitions for an Allen-Cahn model equation.

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Mathematics Subject Classification: Primary: 35J50, 35J60, 58E30, 74N99.

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