# American Institute of Mathematical Sciences

February  2003, 3(1): 1-20. doi: 10.3934/dcdsb.2003.3.1

## Positive entropic schemes for a nonlinear fourth-order parabolic equation

 1 Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain 2 Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany 3 LTCS, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China

Received  March 2002 Revised  July 2002 Published  November 2002

A finite-difference scheme with positivity-preserving and entropy-decreasing properties for a nonlinear fourth-order parabolic equation arising in quantum systems and interface fluctuations is derived. Initial-boundary value problems, the Cauchy problem and a rescaled equation are discussed. Based on this scheme we elucidate properties of the long-time asymptotics for this equation.
Citation: José A. Carrillo, Ansgar Jüngel, Shaoqiang Tang. Positive entropic schemes for a nonlinear fourth-order parabolic equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 1-20. doi: 10.3934/dcdsb.2003.3.1
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