On the slowness of phase boundary motion in one space dimension

Lia Bronsard, Robert V. Kohn

Research output: Contribution to journalArticlepeer-review


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
Issue number8
StatePublished - Dec 1990

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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