A note on the Cahn-Hilliard equation in H 1(ℝ N) involving critical exponent

Title:

A note on the Cahn-Hilliard equation in H 1(ℝ N) involving critical exponent

Creator:

Cholewa, Jan W. and Rodriguez-Bernal, Anibal

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c46974cd-a7a7-47be-b547-04e9daf5d642
uuid:c46974cd-a7a7-47be-b547-04e9daf5d642
doi:10.21136/MB.2014.143854

Subject:

initial value problem for higher order parabolic equations, asymptotic behavior of solutions, and critical exponent

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We consider the Cahn-Hilliard equation in H 1 (ℝ N ) with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as |u| → ∞ and logistic type nonlinearities. In both situations we prove the H 2 (ℝ N )-bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J.W. Cholewa, A. Rodriguez-Bernal (2012).

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

269-283

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false