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M. Bukal, A. Jüngel, D. Matthes:
"A multidimensional nonlinear sixth-order quantum diffusion equation";
Annales de l'Institut Henri Poincaré - Analyse non lineaire, 30 (2013), S. 337 - 365.

Siehe englisches Abstract.

This paper is concerned with the analysis of a sixth-order nonlinear parabolic equation whose solutions describe the evolution of
the particle density in a quantum fluid.We prove the global-in-time existence of weak nonnegative solutions in two and three space
dimensions under periodic boundary conditions. Moreover, we show that these solutions are smooth and classical whenever the
particle density is strictly positive, and we prove the long-time convergence to the spatial homogeneous equilibrium at a universal
exponential rate. Our analysis strongly uses the Lyapunov property of the entropy functional.

Quantum diffusion model; sixth-order equations

http://dx.doi.org/10.1016/j.anihpc.2012.08.003