Publications [#330536] of Jian-Guo Liu

Papers Published
  1. 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. 2220-2245, Society for Industrial & Applied Mathematics (SIAM) [doi] .

    Abstract:
    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. 1771-1784].

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