On the minimal global attractor of a system of phase field equations
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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.
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- 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.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.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.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.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.A. V. Babin and M. I. Vishik, Attractors of Evolution Equations [in Russian], Nauka, Moscow (1989).Google Scholar