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

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January 2008, 21(1): 319-332. doi: 10.3934/dcds.2008.21.319

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, United States
2.	Department of Mathematics, University of Wisconsin-Rock County, Janesville, WI 53546, United States

Received March 2007 Revised June 2007 Published February 2008

Abstract
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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.

Keywords: heteroclinic, Allen-Cahn, minimization., phase transitions.

Mathematics Subject Classification: Primary: 35J50, 35J60, 58E30, 74N9.

Citation: Paul H. Rabinowitz, Ed Stredulinsky. On a class of infinite transition solutions for an Allen-Cahn model equation. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 319-332. doi: 10.3934/dcds.2008.21.319

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