1. A note on the Cahn-Hilliard equation in H 1(ℝ N) involving critical exponent
- Creator:
- Cholewa, Jan W. and Rodriguez-Bernal, Anibal
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- initial value problem for higher order parabolic equations, asymptotic behavior of solutions, and critical exponent
- Language:
- English
- 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).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public