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

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


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  • [1]

    F. Bethuel, G. Orlandi and D. Smets, Slow motion for gradient systems with equal depth multiple-well potentials, J. Differential Equations, 250 (2011), 53-94.


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