Repository: Freie Universität Berlin, Math Department

Averaging of time-periodic dissipation potentials in rate-independent processes

Heida, M. and Mielke, A. (2017) Averaging of time-periodic dissipation potentials in rate-independent processes. Discrete and Continuous Dynamical Systems - Series S, 10 (6). pp. 1303-1327.


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We study the existence and well-posedness of rate-independent systems (or hysteresis operators) with a dissipation potential that oscillates in time with period ε. In particular, for the case of quadratic energies in a Hilbert space, we study the averaging limit ε → 0 and show that the effective dissipation potential is given by the minimum of all friction thresholds in one period, more precisely as the intersection of all the characteristic domains. We show that the rates of the process do not converge weakly, hence our analysis uses the notion of energetic solutions and relies on a detailed estimates to obtain a suitable equi-continuity of the solutions in the limit ε → 0.

Item Type:Article
Additional Information:SFB 1114 Preprint 11/2016 in WIAS Preprint No. 2336
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2178
Deposited By: Silvia Hoemke
Deposited On:16 Jan 2018 10:41
Last Modified:16 Jan 2018 11:06

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