TY - JOUR

T1 - On the slowness of phase boundary motion in one space dimension

AU - Bronsard, Lia

AU - Kohn, Robert V.

PY - 1990/12

Y1 - 1990/12

N2 - 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.

AB - 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.

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U2 - 10.1002/cpa.3160430804

DO - 10.1002/cpa.3160430804

M3 - Article

AN - SCOPUS:84990575560

VL - 43

SP - 983

EP - 997

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 8

ER -