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arXiv · 2010.02532

Singular Neumann boundary problems for a class of fully nonlinear parabolic equations in one dimension

Takashi Kagaya·Qing Liu
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Abstract

In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar curve sliding along the boundary with a zero contact angle, which can be viewed as a limiting model for the capillary phenomenon. We study the uniqueness and existence of solutions by using the viscosity solution theory. We also show the convergence of the solution to a traveling wave as time proceeds to infinity when the initial value is assumed to be convex.

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Takashi Kagaya, Qing Liu. 2020-10-06. Singular Neumann boundary problems for a class of fully nonlinear parabolic equations in one dimension. https://arxiv.org/abs/2010.02532

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