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

Ansgar Jüngel | Zendy; Ingrid Violet | Zendy

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

Author(s) -

Ansgar Jüngel,

Ingrid Violet

Publication year - 2007

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2007.8.861

Subject(s) - mathematics , logarithm , discretization , entropy (arrow of time) , mathematical analysis , dissipation , limit (mathematics) , dimension (graph theory) , boundary value problem , periodic boundary conditions , physics , pure mathematics , quantum mechanics , thermodynamics

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.

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