WIAS Preprint No. 1779, (2013)

Regularity of the solution to a nonstandard system of phase field equations


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K61 35D10 35A02


  • nonstandard phase field system, nonlinear differential equations, initial and boundary value problem, regularity of solutions




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, Krejci, 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.

Appeared in

  • Rend. Cl. Sci. Mat. Nat., 147 (2013) pp. 3--19.

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