Liero, M. and Mielke, A. and Peletier, M. A. and Renger, M. (2017) On microscopic origins of generalized gradient structures. Discrete and Continuous Dynamical Systems  Series S, 10 (1).

PDF
588kB 
Official URL: http://dx.doi.org/10.3934/dcdss.2017001
Abstract
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general nonquadratic dissipation potentials. This paper describes two natural origins for these structures. A first microscopic origin of generalized gradient structures is given by the theory of largedeviation principles. While Markovian diffusion processes lead to classical gradient structures, Poissonian jump processes give rise to coshtype dissipation potentials. A second origin arises via a new form of convergence, that we call EDPconvergence. Even when starting with classical gradient systems, where the dissipation potential is a quadratic functional of the rate, we may obtain a generalized gradient system in the evolutionary Gammalimit. As examples we treat (i) the limit of a diffusion equation having a thin layer of low diffusivity, which leads to a membrane model, and (ii) the limit of diffusion over a high barrier, which gives a reactiondiffusion system.
Item Type:  Article 

Additional Information:  SFB 1114 Preprint 07/2015 in WIAS Preprint No. 2148 Accepted for publication in STAMM DCDSS proceedings 
Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
ID Code:  1889 
Deposited By:  Ulrike Eickers 
Deposited On:  16 Mar 2016 18:34 
Last Modified:  12 Dec 2017 13:38 
Repository Staff Only: item control page