Slow motion for equal depth multiple-well gradient systems: Thedegenerate case

Fabrice Bethuel; Didier Smets

doi:10.3934/dcds.2013.33.67

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2013, Volume 33, Issue 1: 67-87. Doi: 10.3934/dcds.2013.33.67

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Slow motion for equal depth multiple-well gradient systems: The degenerate case

Fabrice Bethuel^1, and
Didier Smets^1,

1.
UPMC-Paris6, UMR 7598 LJLL, Paris, F-75005

Received: April 30, 2011

Revised: November 30, 2011

Published: December 2012

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Abstract

We extend the study [1] of gradient systems with equal depth multiple-well potentials to the case when some of the wells are degenerate, in the sense that the Hessian is non positive at those wells. The exponentially small speed, in terms of distances between fronts, typical of non degenerate potentials is replaced by an algebraic upper bound, whose degree depends on the degeneracy of the wells.

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Mathematics Subject Classification: 35K57, 35B25, 35B36.

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References

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