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# The volume preserving motion by mean curvature as an asymptotic limit of reaction diffusion equations

journal contribution

posted on 1994-01-01, 00:00 authored by Dmitry GolovatyAbstract: "We study the asymptotic limit of the reaction-diffusion equation u[superscript epsilon, subscript t] = [delta] u[superscript epsilon] - 1/2[subscript epsilon]f(u[superscript epsilon]) + 1/[epsilon]g(u[superscript epsilon])[lambda][superscript epsilon] as [epsilon] tends to zero in a radially symmetric domain in R[superscript n] subject to the constraint [f over omega]h(u[superscript epsilon]dx=const. The energy estimates and the signed distance function approach are used to show that a limiting solution can be characterized by moving interfaces. The interfaces evolve by nonlocal (volume preserving) mean curvature flow. Possible interactions between the interfaces are discussed as well."