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期刊名称: Nonlinearity
Volume:28    Issue:6        Page:1963-2001
ISSN:0951-7715

The boundedness-by-entropy method for cross-diffusion systems期刊论文

作者: Jüngel Ansgar
DOI:10.1088/0951-7715/28/6/1963

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页码: 1963-2001
被引频次: 53
出版者: IOP PUBLISHING LTD
期刊名称: Nonlinearity
ISSN: 0951-7715
卷期: Volume:28    Issue:6
语言: English
摘要: The global-in-time existence of bounded weak solutions to a large class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is proved. The main feature of these systems is that the diffusion matrix may be generally neither symmetric nor positive semi-definite. The key idea 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 semi-definite 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. The key conditions for this approach are identified and previous results in the literature are unified and generalized. New existence results are obtained for the population model with or without volume filling.
相关主题: cross-diffusion systems, global existence analysis, nonlinear parabolic systems, entropy method, DISSIPATION, MATHEMATICS, APPLIED, GLOBAL EXISTENCE, CONFINED GEOMETRIES, CHEMOTAXIS, EQUATIONS, PHYSICS, MATHEMATICAL, PARABOLIC-SYSTEMS, CONVERGENCE, POPULATION-MODEL, ION FLUX, POISSON-NERNST-PLANCK,

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