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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

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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