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March/April 2014 Asymptotically self-similar solutions to curvature flow equations with prescribed contact angle and their applications to groove profiles due to evaporation-condensation
Nao Hamamuki
Adv. Differential Equations 19(3/4): 317-358 (March/April 2014).

Abstract

We study the asymptotic behavior of solutions to fully nonlinear second order parabolic equations including a generalized curvature flow equation which was introduced by Mullins in 1957 as a model of evaporation-condensation. We prove that, in the multi-dimensional half space, solutions of the problem with prescribed contact angle asymptotically converge to a self-similar solution of the associated problem under a suitable rescaling. Several properties of the profile function of the self-similar solution are also investigated. We show that the profile function has a corner and that the angles are determined by points at which the equation is degenerate. We also study the depth of the groove, which is represented by the value of the profile function at the boundary. Among other results it turns out that, as the contact angle tends to zero, the depth of the groove is well approximated by the linearized problem.

Citation

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Nao Hamamuki. "Asymptotically self-similar solutions to curvature flow equations with prescribed contact angle and their applications to groove profiles due to evaporation-condensation." Adv. Differential Equations 19 (3/4) 317 - 358, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1295.35089
MathSciNet: MR3161664

Subjects:
Primary: 35B40, 35C06, 35D40, 35K20

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.19 • No. 3/4 • March/April 2014
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