Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Publications [#323246] of Jian-Guo Liu

Papers Published

  1. Liu, JG; Xu, X, Existence theorems for a multidimensional crystal surface model, Siam Journal on Mathematical Analysis, vol. 48 no. 6 (January, 2016), pp. 3667-3687, Society for Industrial & Applied Mathematics (SIAM) [doi]
    (last updated on 2019/05/24)

    Abstract:
    © 2016 Society for Industrial and Applied Mathematics. In this paper we study the existence assertion of the initial boundary value problem for the equation @u/@t = Δe-Δu. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow "cancels" it out. The net result is that we obtain a solution u that satisfies the equation and the initial boundary conditions in the almost everywhere (a.e.) sense.

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320