Author(s)

G. Caginalp & H. Merdan

Abstract

Renormalization methods and interface problems G. Caginalp & H. Merdan Department of Mathematics, University of Pittsburgh Pittsburgh, U. S.A Abstract The application of renormalization techniques to interface problems is considered after a brief review of the methodology. We study the standard sharp interface problem in the quasi-static limit (time derivative set to zero in the heat equation) for large time. The characteristic length, R(t), behaves as tP where P has values in the continuous spectrum [1/3,1/2] when the dynamical undercooling is nonzero, and /I E [1/3, co) when the undercooling is set at zero. The value of p = 1. obtained by Jasnow and Vinals is extracted from this spectrum as a consequence of boundary conditions that impose a plane wave. In almost all of these cases, the capillarity length is an irrelevant variable for large time, in sharp contrast to its role in linear stability for short time. 1 Introduction Renormalization group and scaling methods (RG) originated as part

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