Repository: Freie Universit├Ąt Berlin, Math Department

A gradient system with a wiggly energy and relaxed EDP-convergence

Dondl, Patrick and Frenzel, Thomas and Mielke, Alexander (2019) A gradient system with a wiggly energy and relaxed EDP-convergence. ESAIM Control Optimisation and Calculus of Variations, 25 (68). pp. 1-45.

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Official URL: http://DOI:10.1051/cocv/2018058

Abstract

If gradient systems depend on a microstructure, we want to derive a macroscopic gradient structure describing the effective behavior of the microscopic system. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gammaconvergence. We call this notion relaxed EDP-convergence since the special structure of the dissipation functional may not be preserved under Gamma-convergence. However, by investigating the kinetic relation we derive the macroscopic dissipation potential.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2662
Deposited By: Monika Drueck
Deposited On:17 Jan 2022 16:45
Last Modified:18 Mar 2022 09:57

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