Heida, M. and Mielke, A. (2017) Averaging of timeperiodic dissipation potentials in rateindependent processes. Discrete and Continuous Dynamical Systems  Series S, 10 (6). pp. 13031327.

PDF
4MB 
Official URL: http://dx.doi.org/10.3934/dcdss.2017070
Abstract
We study the existence and wellposedness of rateindependent 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 equicontinuity 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 
Repository Staff Only: item control page