Averaging of time-periodic dissipation potentials in rate-independent processes
- Heida, Martin
- Mielke, Alexander
2010 Mathematics Subject Classification
- 34C55 47J20 49J40 74N30
- Rate-independent systems, play operator with time-dependent thresholds, energetic solutions, locomotion
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.
- Discrete Contin. Dyn. Syst. Ser. S, 10 (2017), pp. 1303--1327.