Complex transient patterns on the disk

36. Jonathan P. Desi, Evelyn Sander, Thomas Wanner:
    Complex transient patterns on the disk
    Discrete and Continuous Dynamical Systems, Series A 15(4), pp. 1049-1078, 2006.

Abstract

This paper studies spinodal decomposition in the Cahn-Hilliard model on the unit disk. It has previously been shown that starting at initial conditions near a homogeneous equilibrium on a rectangular domain, solutions to the linearized and the nonlinear Cahn-Hilliard equation behave indistinguishably up to large distances from the homogeneous state. In this paper we demonstrate how these results can be extended to nonrectangular domains. Particular emphasis is put on the case of the unit disk, for which interesting new phenomena can be observed. Our proof is based on vector-valued extensions of probabilistic methods used in Wanner (2004). These are the first results of this kind for domains more general than rectangular.

Links

The published version of the paper can be found at https://doi.org/10.3934/dcds.2006.15.1049.

Bibtex

@article{desi:sander:wanner:06a,
   author = {Jonathan P. Desi and Evelyn Sander and Thomas Wanner},
   title = {Complex transient patterns on the disk},
   journal = {Discrete and Continuous Dynamical Systems, Series A},
   year = 2006,
   volume = 15,
   number = 4,
   pages = {1049--1078},
   doi = {10.3934/dcds.2006.15.1049}
   }