On the slowness of phase boundary motion in one space dimension
- 1 December 1990
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 43 (8) , 983-997
- https://doi.org/10.1002/cpa.3160430804
Abstract
We study the limiting behavior of the solution ofwith 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.,uϵ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ϵ → 0, the solution maintains its transition layer structure, and the transition points move slower than any power of ϵ.Keywords
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