On the slowness of phase boundary motion in one space dimension

Lia Bronsard, Robert Kohn

Research output: Contribution to journalArticle

Abstract

We study the limiting behavior of the solution of (Formula Presented.) 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., 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.

Original languageEnglish (US)
Pages (from-to)983-997
Number of pages15
JournalCommunications on Pure and Applied Mathematics
Volume43
Issue number8
DOIs
StatePublished - 1990

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Transition Layer
Phase boundaries
Dirichlet conditions
Motion
Limiting Behavior
Energy Method
Neumann Boundary Conditions
Boundary conditions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the slowness of phase boundary motion in one space dimension. / Bronsard, Lia; Kohn, Robert.

In: Communications on Pure and Applied Mathematics, Vol. 43, No. 8, 1990, p. 983-997.

Research output: Contribution to journalArticle

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