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On a nonlinear parabolic equation arising from anisotropic plane curve evolution
Journal article   Peer reviewed

On a nonlinear parabolic equation arising from anisotropic plane curve evolution

Chi-Cheung Poon and Dong-Ho Tsai
Journal of Differential Equations, Vol.258(7), pp.2375-2407
05/04/2015

Abstract

Anisotropic plane curve evolution Self-similar solution Translational self-similar solution Type-one blow-up Type-two blow-up
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.

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