Mielke, Alexander
(2023)
*Non-equilibrium steady states as saddle points and EDP-convergence for slow-fast gradient systems.*
Journal of Mathematical Physics, 64
(12).

Full text not available from this repository.

Official URL: https://doi.org/10.1063/5.0149910

## Abstract

The theory of slow-fast gradient systems leads in a natural way to non-equilibrium steady states, because on the slow time scale the fast subsystem stays in steady states that are controlled by the interaction with the slow system. Using the theory of convergence of gradient systems depending on a small parameter ɛ (here the ratio between the slow and the fast time scale) in the sense of the energy-dissipation principle shows that there is a natural characterization of these non-equilibrium steady states as saddle points of a so-called B-function where the slow variables are fixed. We give applications to slow-fast reaction-diffusion systems based on the so-called cosh-type gradient structure for reactions. It is shown that two binary reactions give rise to a ternary reaction with a state-dependent reaction coefficient. Moreover, we show that a reaction-diffusion equation with a thin membrane-like layer convergences to a transmission condition, where the formerly quadratic dissipation potential for diffusion convergences to a cosh-type dissipation potential for the transmission in the membrane limit.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3171 |

Deposited By: | Lukas-Maximilian Jaeger |

Deposited On: | 04 Sep 2024 11:16 |

Last Modified: | 04 Sep 2024 11:16 |

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