Finite dimensional exponential attractor for the phase field model

Abstract

We consider the phase field equations in arbitrary space dimension. We show that the corresponding boundary value problems are well-posed when assuming that the initial data is square integrable and prove the existence of a maximal attractor and of an inertial set.

Keywords:

• Phase field
• parabolic system
• semigroup
• inertial set
• maximal attractor

¹The authors are grateful to F. Abergel for many inspiring discussions

¹The authors are grateful to F. Abergel for many inspiring discussions

²The author is partially supported by the Sloan Doctoral Dissertation Fellowship for the academic year 1990-1991 and the NSF grant DMS-86-12880 in the summer of 1991

¹The authors are grateful to F. Abergel for many inspiring discussions

¹The authors are grateful to F. Abergel for many inspiring discussions

²The author is partially supported by the Sloan Doctoral Dissertation Fellowship for the academic year 1990-1991 and the NSF grant DMS-86-12880 in the summer of 1991

Notes

¹The authors are grateful to F. Abergel for many inspiring discussions

¹The authors are grateful to F. Abergel for many inspiring discussions

²The author is partially supported by the Sloan Doctoral Dissertation Fellowship for the academic year 1990-1991 and the NSF grant DMS-86-12880 in the summer of 1991