Weierstraß-Institut für Angewandte Analysis und Stochastik, , Mohrenstraße 39, 10117 Berlin, Germany.
Philos Trans A Math Phys Eng Sci. 2013 Nov 18;371(2005):20120346. doi: 10.1098/rsta.2012.0346. Print 2013 Dec 28.
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 λ-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.
我们将反应扩散方程组视为相对于熵泛函和耗散度量的梯度系统，其中耗散度量是由所谓的 Onsager 算子给出的，该算子是 Wasserstein 型扩散部分和反应部分的和。我们提供了通过纯粹微分方法建立熵泛函测地 λ-凸性的方法，从而避免了从质量输运角度的论证。最后，包括漂移扩散系统在内的几个例子提供了该理论的适用性的概述。
