Article Contents
Article Contents

# Positive entropic schemes for a nonlinear fourth-order parabolic equation

• 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.
Mathematics Subject Classification: 65M06, 35G25.

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