LONG TIME BEHAVIOR OF AN ALLEN-CAHN TYPE EQUATION WITH A SINGULAR POTENTIAL AND DYNAMIC BOUNDARY CONDITIONS

Haydi Israel

doi:10.11948/2012003

2012 Volume 2 Issue 1

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Haydi Israel. LONG TIME BEHAVIOR OF AN ALLEN-CAHN TYPE EQUATION WITH A SINGULAR POTENTIAL AND DYNAMIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 29-56. doi: 10.11948/2012003

Citation:

Haydi Israel. LONG TIME BEHAVIOR OF AN ALLEN-CAHN TYPE EQUATION WITH A SINGULAR POTENTIAL AND DYNAMIC BOUNDARY CONDITIONS[J]. Journal of Applied Analysis & Computation, 2012, 2(1): 29-56. doi: 10.11948/2012003

LONG TIME BEHAVIOR OF AN ALLEN-CAHN TYPE EQUATION WITH A SINGULAR POTENTIAL AND DYNAMIC BOUNDARY CONDITIONS

Haydi Israel

Laboratoire de Mathématiques et Applications, Université de Poitiers, UMR CNRS 7348-SP2 MI, Boulevard Marie et Pierre Curie-Téléport 2, BP 30179-86962 Futuroscope Chasseneuil Cedex, France

Abstract

Abstract

The aim of this paper is to study the well-posedness and the long time behavior of solutions for an equation of Allen-Cahn type owing to proper approximations of the singular potential and a suitable definition of solutions. We also prove the existence of the finite dimensional global attractor as well as exponential attractors.
- Allen-Cahn equation /
- dynamic boundary conditions /
- singular potentials /
- variational solutions /
- global attractor /
- exponential attractors
MSC: 35B40;35B41;35K55;35J60;80A22

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References

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