Regularity and approximation of strong solutions to 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%2F17%3A10372070" target="_blank" >RIV/00216208:11320/17:10372070 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/S0218202517500518" target="_blank" >http://dx.doi.org/10.1142/S0218202517500518</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218202517500518" target="_blank" >10.1142/S0218202517500518</a>
Alternative languages
Result language
angličtina
Original language name
Regularity and approximation of strong solutions to rate-independent systems
Original language description
Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this work, we prove the existence of Holder-regular strong solutions for a class of rate-independent systems. We also establish additional higher regularity results that guarantee the uniqueness of strong solutions. The proof proceeds via a time-discrete Rothe approximation and careful elliptic regularity estimates depending in a quantitative way on the (local) convexity of the potential featuring in the model. In the second part of the paper, we show that our strong solutions may be approximated by a fully discrete numerical scheme based on a spatial finite element discretization, whose rate of convergence is consistent with the regularity of strong solutions whose existence and uniqueness are established.
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Models and Methods in Applied Sciences
ISSN
0218-2025
e-ISSN
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Volume of the periodical
27
Issue of the periodical within the volume
13
Country of publishing house
SG - SINGAPORE
Number of pages
46
Pages from-to
2511-2556
UT code for WoS article
000413371300005
EID of the result in the Scopus database
2-s2.0-85030840996