1998 A convolution model for interfacial motion: the generation and propagation of internal layers in higher space dimensions
Paul C. Fife, Xuefeng Wang
Adv. Differential Equations 3(1): 85-110 (1998). DOI: 10.57262/ade/1366399906

Abstract

Properties of solutions of a bistable nonlinear convolution equation in higher space dimensions are studied. The nonlinearity is the derivative of a double well function. The theory of traveling waves for this equation was given in a previous publication ([4]). Here we consider spreading phenomena for state regions, in some cases by means of the motion of domain walls, which are modeled by internal layers. These phenomena are analogous to those known for the bistable nonlinear diffusion equation, and in particular, for the Allen--Cahn equation, which is a model for the motion of some grain boundaries in solid materials. Cases when the two wells have unequal depth are considered, as well as when they have equal depth. In the latter case a motion-by-curvature law is derived formally in two space dimensions.

Citation

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Paul C. Fife. Xuefeng Wang. "A convolution model for interfacial motion: the generation and propagation of internal layers in higher space dimensions." Adv. Differential Equations 3 (1) 85 - 110, 1998. https://doi.org/10.57262/ade/1366399906

Information

Published: 1998
First available in Project Euclid: 19 April 2013

zbMATH: 0954.35087
MathSciNet: MR1608081
Digital Object Identifier: 10.57262/ade/1366399906

Subjects:
Primary: 45K05
Secondary: 35K55 , 35Q72 , 73B30 , 82B24

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.3 • No. 1 • 1998
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