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
SN - 0010-3640
VL - 43
SP - 983
EP - 997
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 8
ER -