Journal of Mathematical Sciences

, Volume 70, Issue 3, pp 1767–1777

On the minimal global attractor of a system of phase field equations

  • V. K. Kalantarov
Article
  • 31 Downloads

Abstract

The unique global solvability of the initial-boundary value problem (1)–(3) is proved for the system of phase field equations (1), (2). It is shown that the problem (1)–(3) generates a continuous compact semigroup Vt, t>0, for which there exists a minimal global B-attractor.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Caginalp, “An analysis of a phase field model of a free boundary,” Arch. Rational Mech. Anal.92, 205–245 (1986).CrossRefGoogle Scholar
  2. 2.
    G. Caginalp and S. Hastings, “Properties of some ordinary differential equations related to free boundary problems,” Proc. Roy. Soc. Edinburgh,104A, 217–234 (1986).Google Scholar
  3. 3.
    C. M. Elliott and Song Mu Zheng, “Global existence and stability of solutions to the phase field equations,” in: Free Boundary Value Problems (Oberwolfach, 1989), Internat. Ser. Numer. Math., 95, BirkhÄuser, Basel (1990), pp. 46–58.Google Scholar
  4. 4.
    O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence (1968).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya, “On the determination of minimal global attractors for the Navier-Stokes and other partial differential equations,” Usp. Mat. Nauk,42, No. 6, 25–60 (1987).Google Scholar
  6. 6.
    O. A. Ladyzhenskaya, “Some complements and corrections to my papers on the theory of attractors for abstracts semigroups,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,182, 102–112 (1990).Google Scholar
  7. 7.
    A. V. Babin and M. I. Vishik, Attractors of Evolution Equations [in Russian], Nauka, Moscow (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • V. K. Kalantarov

There are no affiliations available

Personalised recommendations