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Gradient structures and geodesic convexity for reaction-diffusion systems
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DOI：10.1098/rsta.2012.0346.png)
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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.
Keyword:
geodesic convexity
gradient structures
Onsager operator
reaction-diffusion system
Wasserstein metric
relative entropy
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