Long time behaviour of a Cahn–Hilliard system coupled with viscoelasticity

Tom 98 / 2010

Irena Paw/low, Wojciech M. Zaj/aczkowski Annales Polonici Mathematici 98 (2010), 1-21 MSC: 35K50, 35K60, 35L20, 35Q72. DOI: 10.4064/ap98-1-1

Streszczenie

The long-time behaviour of a unique regular solution to the Cahn–Hilliard system coupled with viscoelasticity is studied. The system arises as a model of the phase separation process in a binary deformable alloy. It is proved that for a sufficiently regular initial data the trajectory of the solution converges to the $\omega $-limit set of these data. Moreover, it is shown that every element of the $\omega $-limit set is a solution of the corresponding stationary problem.

Autorzy

  • Irena Paw/lowSystems Research Institute
    Polish Academy of Sciences
    Newelska 6
    01-447 Warszawa, Poland
    and
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail
  • Wojciech M. Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-956 Warszawa, Poland
    and
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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