American Institute of Mathematical Sciences

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

Positive entropic schemes for a nonlinear fourth-order parabolic equation

José A. Carrillo 1, , Ansgar Jüngel 2, and  Shaoqiang Tang 3,

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.
Keywords: long-time behavior of discrete solutions., Finite difference method, discrete entropy estimates, discrete positive solutions.
Mathematics Subject Classification: 65M06, 35G2.
Citation: José A. Carrillo, Ansgar Jüngel, Shaoqiang Tang. Positive entropic schemes for a nonlinear fourth-order parabolic equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 1-20. doi: 10.3934/dcdsb.2003.3.1
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