Nonlocal reaction--diffusion equations and nucleation |
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| Authors: | RUBINSTEIN, JACOB STERNBERG, PETER |
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| Affiliation: | Department of Mathematics, Technion—Israel Institute of Technology Haifa 32000, Israel
Department of Mathematics, Indiana University Bloomington, Indiana 47405, USA |
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| Abstract: | A nonlocal reaction-diffusion equation is presented and analysedusing matched asymptotic expansions and multiple timescales.The problem models a binary mixture undergoing phase separation.The particular form of the equation is motivated by argumentsfrom the calculus of variations, with the nonlocality arisingfrom an enforcement of conservation of mass. It is shown thatthe evolution of the solution can be characterized by trackingthe motion of fronts separating phases. The propagation of theinterfaces is found to be a coarsening process which dependsin a nonlocal fashion on mean curvature. Several special featuresof the equations of motion for the fronts are studied, and therelation of this evolution to Cahn-Hilliard theory and nucleationis discussed |
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