Geodesic
BV solutions constructed using the epsilon-neighborhood method
Minh, Mach Nguyet1
1 Department of Mathematics, University of Stuttgart, Allmandring 5b, 70569 Stuttgart, Germany.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 188-207

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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)].

Reçu le :
DOI : 10.1051/cocv/2015001
Classification : 49M99, 49J20
Keywords: Rate-independent systems, BV solutions, local minimizers, energy-dissipation balance

Minh, Mach Nguyet 1

1 Department of Mathematics, University of Stuttgart, Allmandring 5b, 70569 Stuttgart, Germany. 
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     title = {BV solutions constructed using the epsilon-neighborhood method},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {188--207},
     publisher = {EDP-Sciences},
     volume = {22},
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     mrnumber = {3489382},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015001/}
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Minh, Mach Nguyet. BV solutions constructed using the epsilon-neighborhood method. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 1, pp. 188-207. doi: 10.1051/cocv/2015001

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