Contributions to Books:
A. Jüngel, N. Zamponi:
"A cross-difussion system derived from a Fokker-Planck equation with partial averaging";
in: "ASC Report 2/2016",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
A cross-diﬀusion system for two compoments with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated to a multi-dimensional Ito process, assuming that the diﬀusion coeﬃcients depend on partial averages of the probability density with exponential weights. A main feature is that the diﬀusion matrix of the limiting cross-diﬀusion system is generally neither symmetric nor positive deﬁnite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.