Publications in Scientific Journals:
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),
337
- 365.
English 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.
German abstract:
Siehe englisches Abstract.
Keywords:
Quantum diffusion model; sixth-order equations
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.anihpc.2012.08.003
Created from the Publication Database of the Vienna University of Technology.