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Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 35G25, 35B40, 35B65, 35Q40.

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