|
Hokkaido University Collection of Scholarly and Academic Papers >
Research Institute for Electronic Science >
Peer-reviewed Journal Articles, etc >
Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems
| Title: | Higher dimensional SLEP equation and applications to morphological stability in Polymer Problems |
| Authors: | Nishiura, Yasumasa Browse this author →KAKEN DB | | Suzuki, Hiromasa Browse this author |
| Keywords: | singular perturbation | | diblock copolymer | | reaction diffusion system | | pattern formation | | matched asymptotic expansion | | stability | | critical eigenvalues | | AMS subject classification = 35B25 | | AMS subject classification = 35B35 | | AMS subject classification = 35K57 |
| Issue Date: | 2005 |
| Publisher: | Society for Industrial and Applied Mathematics |
| Journal Title: | SIAM Journal on Mathematical Analysis |
| Volume: | 36 |
| Issue: | 3 |
| Start Page: | 916 |
| End Page: | 966 |
| Publisher DOI: | 10.1137/S0036141002420157 |
| Abstract: | Existence and stability of stationary internal layered solutions to a rescaled diblock copolymer equation are studied in higher dimensional space. Rescaling is necessary since the characteristic domain size of any stable pattern eventually vanishes in an appropriate singular limit. A general sufficient condition for the existence of singularly perturbed solutions and the associated stability criterion are given in the form of linear operators acting only on the limiting location of the interface. Applying the results to radially symmetric and planar patterns, we can show, for instance, stability of radially symmetric patterns when one of the components of diblock copolymer dominates the other, and that of the long-striped pattern in a long and narrow domain for the planar case. These results are consistent with the experimental ones. The above existence and stability criterion can be easily extended to a class of reaction diffusion systems of activator-inhibitor type. |
| Rights: | © 2004 Society for Industrial and Applied Mathematics |
| Type: | article |
| URI: | http://hdl.handle.net/2115/35224 |
| Appears in Collections: | 電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
|
Submitter: 西浦 廉政
|
