# American Institute of Mathematical Sciences

November  2007, 8(4): 861-877. doi: 10.3934/dcdsb.2007.8.861

## First-order entropies for the Derrida-Lebowitz-Speer-Spohn equation

 1 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Wien, Austria 2 Laboratoire de Mathématiques Appliquées, CNRS UMR 6620, Université Blaise Pascal (Clermont-Ferrand 2), 63177 Aubière, France

Received  January 2007 Revised  July 2007 Published  August 2007

A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is analyzed. Using a new semi-discrete approximation in time, a first-order entropy–entropy dissipation inequality is proved. Passing to the limit of vanishing time discretization parameter, some regularity results are deduced. Moreover, it is shown that the solution is strictly positive for large time if it does so initially.
Citation: Ansgar Jüngel, Ingrid Violet. First-order entropies for the Derrida-Lebowitz-Speer-Spohn equation. Discrete & Continuous Dynamical Systems - B, 2007, 8 (4) : 861-877. doi: 10.3934/dcdsb.2007.8.861
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