Math @ Duke

Publications [#330536] of JianGuo Liu
Papers Published
 Liu, JG; Xu, X, Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions,
Siam Journal on Mathematical Analysis, vol. 49 no. 3
(January, 2017),
pp. 22202245, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/06/17)
Abstract: © 2017 Society for Industrial and Applied Mathematics. In this paper we are concerned with the existence of a weak solution to the initial boundary value problem for the equation ∂u/∂t = Δ(Δu)3. This problem arises in the mathematical modeling of the evolution of a crystal surface. Existence of a weak solution u with Δu ≥ 0 is obtained via a suitable substitution. Our investigations reveal the close connection between this problem and the equation ∂tρ+ρ2Δ2ρ3 = 0, another crystal surface model first proposed by H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare [Phys. D, 240 (2011), pp. 17711784].


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