Global attractors for Cahn-Hilliard equations with non constant mobility

Details Global attractors for Cahn-Hilliard equations with non constant mobility Global attractors for Cahn-Hilliard equations with non constant mobility

2007-02-26

arxiv.org/abs/math/0702791v1

Mathematics

Analysis of PDEs

Scientific paper

10.1088/0951-7715/20/10/006

We address, in a three-dimensional spatial setting, both the viscous and the standard Cahn-Hilliard equation with a nonconstant mobility coefficient. As it was shown in J.W. Barrett and J.W. Blowey, Math. Comp., 68 (1999), 487-517, one cannot expect uniqueness of the solution to the related initial and boundary value problems. Nevertheless, referring to J. Ball's theory of generalized semiflows, we are able to prove existence of compact quasi-invariant global attractors for the associated dynamical processes settled in the natural "finite energy" space. A key point in the proof is a careful use of the energy equality, combined with the derivation of a "local compactness" estimate for systems with supercritical nonlinearities, which may have an independent interest. Under growth restrictions on the configuration potential, we also show existence of a compact global attractor for the semiflow generated by the (weaker) solutions to the nonviscous equation characterized by a "finite entropy" condition.

Affiliated with

Also associated with

No associations

Rating

Global attractors for Cahn-Hilliard equations with non constant mobility does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Global attractors for Cahn-Hilliard equations with non constant mobility, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global attractors for Cahn-Hilliard equations with non constant mobility will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-131844