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Equations with singular diffusivity

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Title: Equations with singular diffusivity
Authors: Kobayashi, R. Browse this author
Giga, Y. Browse this author
Keywords: singular diffusivity
faceted growth
grain boundary
extended gradient system
Issue Date: 1-Aug-1998
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 420
Start Page: 1
End Page: 45
Abstract: Recently the models of the faceted crystal growth and of the grain boundary were proposed based on the gradient system with nondifferentiable energy. In this article, we study their most basic forms given by the equations ut = (ux/|ux|)x and ut = a/1(a * ux / ux)x where both of the related energy include luxl term of power one which is nondiffer­ entiable at Ux = 0. The first equation is spatially homogeneous while the second one is spatially inhomogeneous when a depends on x. These equations naturally express non-local interactions through their singular diffusivities ( Ux = 0) which make the profiles of the solutions completely flat. Mathematical basis for justifying and analyzing these equations will be explained, and also it will be shown how the solutions of the equations evolve by theoretical and numerical approach.
Type: bulletin (article)
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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