# zbMATH — the first resource for mathematics

Stability of Cahn-Hilliard fronts. (English) Zbl 0939.35022
The Cahn-Hilliard equation on the real axis $\partial _t u=\partial _x ^2 (-\partial _x^2 u-u/2+u^3/3)$ is considered. Stability of the kink solution is proved. The proof is based on an inductive renormalization group method. In addition, the detailed asymptotic of the solution is obtained as time tends to infinity.

##### MSC:
 35B35 Stability in context of PDEs 35K25 Higher-order parabolic equations
Full Text:
##### References:
 [1] Alikakos, Arch Rational Mech Anal 128 pp 165– (1994) [2] Bray, Adv in Phys 43 pp 357– (1994) [3] Bricmont, Comm Pure Appl Math 47 pp 893– (1994) [4] Caffarelli, Arch Rational Mech Anal 133 pp 129– (1995) [5] Pego, Proc Roy Soc London Ser A 422 pp 261– (1989) [6] Pego, Philos Trans Roy Soc London Ser A 340 pp 47– (1992) [7] Shinozaki, Phys Rev E 47 pp 804– (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.