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Author: Colli, Pierluigi × Subject: nonlinear differential equations ×

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    Regularity of the solution to a nonstandard system of phase field equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen
    A nonstandard systems of differential equations describing two-species phase segregation is considered. This system naturally arises in the asymptotic analysis recently done by Colli, Gilardi, Krej¡cí, and Sprekels as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, a well-posedness result is proved for the limit system. This paper deals with the above limit problem in a less general but still very significant framework and provides a very simple proof of further regularity for the solution. As a byproduct, a simple uniqueness proof is given as well.
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    A continuous dependence result for a nonstandard system of phase field equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Colli, Pierluigi; Gilardi, Gianni; Krejcí, Pavel; Sprekels, Jürgen
    The present note deals with a nonstandard systems of differential equations describing a two-species phase segregation. This system naturally arises in the asymptotic analysis carried out recently by the same authors, as the diffusion coefficient in the equation governing the evolution of the order parameter tends to zero. In particular, an existence result has been proved for the limit system in a very general framework. On the contrary, uniqueness was shown by assuming a constant mobility coefficient. Here, we generalize this result and prove a continuous dependence property in the case that the mobility coefficient suitably depends on the chemical potential