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arXiv · 1612.04269

Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions

Jian-Guo Liu·Xiangsheng Xu
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Abstract

In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation $\frac{\partial u}{\partial t} = Δ\left(Δu\right)^{-3}$. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution $u$ with $Δu\geq 0$ is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation $\partial_tρ+ρ^2Δ^2ρ^3=0$, another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn and J. Weare in Physica D: Nonlinear Phenomena, bf 240 (2011), no. 21, 1771-1784.

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Jian-Guo Liu, Xiangsheng Xu. 2017-05-31. Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions. https://arxiv.org/abs/1612.04269

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