A. Jüngel:

"The boundedness-by-entropy principle for cross-diffusion systems";

in: "ASC Report 19/2014", Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 38.

A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that the diffusion matrix may

be generally neither symmetric nor positive semi-definite. The key idea of the principle is to employ a transformation of variables, determined by the entropy density, which is defined by

the gradient-flow formulation. The transformation yields at the same time a positive semidefinite diffusion matrix, suitable gradient estimates as well as lower and/or upper bounds of the solutions. These bounds are a consequence of the transformation of variables and are obtained without the use of a maximum principle. Several classes of cross-diffusion systems are identified which can be solved by this technique. The systems are formally derived from continuous-time random walks on a lattice modeling, for instance, the motion of ions, cells, or fluid particles.

Strongly coupled parabolic systems, global-in-time existence, bounded weak solutions, gradient flow, entropy variables, entropy method, volume-filling effects, population dynamics models, non-equilibrium thermodynamics

http://www.asc.tuwien.ac.at/preprint/2014/asc20x2014.pdf

Created from the Publication Database of the Vienna University of Technology.