Two-Speed Solutions to Non-convex Rate-Independent Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10441308" target="_blank" >RIV/00216208:11320/21:10441308 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1JfHAdHoYn" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=1JfHAdHoYn</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-020-01599-z" target="_blank" >10.1007/s00205-020-01599-z</a>
Alternative languages
Result language
angličtina
Original language name
Two-Speed Solutions to Non-convex Rate-Independent Systems
Original language description
We consider evolutionary PDE inclusions of the form -λu.λ+Δu-DW0(u)+fCONTAINS AS MEMBERPARTIAL DIFFERENTIALR1(u.)in(0,T)xΩ,where R1 is a positively 1-homogeneous rate-independent dissipation potential and W is a (generally) non-convex energy density. This work constructs solutions to the above system in the slow-loading limit λDOWNWARDS ARROW 0. Our solutions have more regularity both in space and time than those that have been obtained with other approaches. On the "slow" time scale we see strong solutions to a purely rate-independent evolution. Over the jumps, we obtain a detailed description of the behavior of the solution and we resolve the jump transients at a "fast" time scale, where the original rate-dependent evolution is still visible. Crucially, every jump transient splits into a (possibly countable) number of rate-dependent evolutions, for which the energy dissipation can be explicitly computed. This, in particular, yields a global energy equality for the whole evolution process. It also turns out that there is a canonical slow time scale that avoids intermediate-scale effects, where movement occurs in a mixed rate-dependent/rate-independent way. In this way, we obtain precise information on the impact of the approximation on the constructed solution. Our results are illustrated by examples, which elucidate the effects that can occur.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
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Volume of the periodical
239
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
65
Pages from-to
1667-1731
UT code for WoS article
000606170800002
EID of the result in the Scopus database
2-s2.0-85098972134