| Issue |
ESAIM: COCV
Volume 22, Number 1, January-March 2016
|
|
|---|---|---|
| Page(s) | 188 - 207 | |
| DOI | https://doi.org/10.1051/cocv/2015001 | |
| Published online | 15 January 2016 | |
BV solutions constructed using the epsilon-neighborhood method∗, ∗∗, ∗∗∗
Department of Mathematics, University of Stuttgart,
Allmandring 5b, 70569
Stuttgart,
Germany.
machnt@mathematik.uni-stuttgart.de
Received:
13
February
2013
Revised:
17
June
2014
We study a certain class of weak solutions to rate-independent systems, which is constructed by using the local minimality in a small neighborhood of order ε and then taking the limit ε → 0. We show that the resulting solution satisfies both the weak local stability and the new energy-dissipation balance, similarly to the BV solutions constructed by vanishing viscosity introduced recently by Mielke et al. [A. Mielke, R. Rossi and G. Savaré, Discrete Contin. Dyn. Syst. 2 (2010) 585–615; ESAIM: COCV 18 (2012) 36–80; To appear in J. Eur. Math. Soc. (2016)].
Mathematics Subject Classification: 49M99 / 49J20
Key words: Rate-independent systems / BV solutions / local minimizers / energy-dissipation balance
I would like to express my deep gratitude to Professor Giovanni Alberti for proposing the problem to me and giving many helpful discussions. I sincerely thank Professor Riccarda Rossi, Li-Chang Hung and Tran Minh-Binh for their helpful comments and remarks.
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.