WIAS Preprint No. 1580, (2010)

A nonlocal quasilinear multi-phase system with nonconstant specific heat and heat conductivity


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Sprekels, Jürgen

2010 Mathematics Subject Classification

  • 35K51 35K59 35K65 45K05 80A22


  • Phase transitions, nonlocal, models, quasilinear, integrodifferential vectorial, equation




In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a quasilinear internal energy balance ruling the evolution of the absolute temperature with a vectorial integro-differential inclusion governing the (vectorial) phase-parameter dynamics. The specific heat and the heat conductivity $k$ are allowed to depend both on the order parameter $chi$ and on the absolute temperature $theta$ of the system, and the convex component of the free energy may or may not be singular. Uniqueness and continuous data dependence are also proved under additional assumptions.

Appeared in

  • J. Differential Equations, 251 (2011) pp. 1354--1387.

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