Contributions to Books:
"Cross-diffusion systems with entropy structure";
in: "ASC Report 19/2017",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Some results on cross-diﬀusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diﬀusion opera-tors, due to Amann, and global-in-time existence theorems by Lepoutre, Moussa, and co-workers for cross-diﬀusion systems with an additional Laplace structure. The boundedness-by-entropy method allows for global bounded weak solutions to certain diﬀusion systems. Furthermore, a partial result on the uniqueness of weak solutions is recalled, and some open problems are presented.
Strongly coupled parabolic systems, local existence of solutions, global existence of solutions, gradient ﬂow, duality method, boundedness-by-entropy method, nonlinear Aubin-Lions lemma, Kullback-Leibler entropy.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.