Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 371, Issue 2005, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsta.2012.0346
Keywords
geodesic convexity; gradient structures; Onsager operator; reaction-diffusion system; Wasserstein metric; relative entropy
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Funding
- DFG via the Matheon project [D22]
- ERC-AdG [267802]
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We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.
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