A. Jüngel, I. Violet:

"First-order entropies for the Derrida-Lebowitz-Speer-Spohn equation";

in: "ASC Report 10/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

A logarithmic fourth-order parabolic equation in one space dimension

with periodic boundary conditions is analyzed. Using a new semidiscrete

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.

Entropy-entropy dissipation inequality, existence of weak solutions, regularity

http://www.asc.tuwien.ac.at/preprint/2007/asc10x2007.pdf

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