WIAS Preprint No. 1602, (2011)

Well-posedness and long-time behavior for a nonstandard viscous Cahn--Hilliard system


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

2010 Mathematics Subject Classification

  • 74A15 35K55 35A05, 35B40


  • Cahn-Hilliard equation, phase field model, well-posedness, long-time behavior




We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a careful development of uniform estimates and the deduction of certain useful boundedness properties, we prove existence and uniqueness of a global-in-time smooth solution to the associated initial/boundary-value problem; moreover, we give a description of the relative $omega$-limit set.

Appeared in

  • SIAM J. Appl. Math., 71 (2011) pp. 1849--1870.

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