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On the slowness of phase boundary motion in one space dimension

โœ Scribed by Lia Bronsard; Robert V. Kohn

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
532 KB
Volume
43
Category
Article
ISSN
0010-3640

No coin nor oath required. For personal study only.

โœฆ Synopsis

We study the limiting behavior of the solution of

with a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on "energy methods". We assume that the initial data has a "transition layer structure", i.e., u' = f 1 except near finitely many transition points. We show that, in the limit as c + 0, the solution maintains its transition layer structure, and the transition points move slower than any power of e . Our work is closely related to that of Neu [ 221, Cam and Peg0 [ 5 1, [ 6 1, and Fusco and Hale [ 1 I], [ 121. Neu uses the method of matched asymptotic expansions

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