Article ID Journal Published Year Pages File Type
4610066 Journal of Differential Equations 2015 33 Pages PDF
Abstract

We study the asymptotic behavior of a nonlinear parabolic equation arising from anisotropic plane curve evolution. We show that, if the solution has type-one blow-up, then it will converge (after rescaling) to a self-similar solution. If the solution has type-two blow-up, then its profile near the maximum point is also known. In the case of anisotropic plane curve evolution, if the evolving curve has type-two blow-up, then it will converge to a translational self-similar solution.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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