Curvature driven flow of a family of interacting curves with applications
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00346329" target="_blank" >RIV/68407700:21340/20:00346329 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mma.6182" target="_blank" >https://doi.org/10.1002/mma.6182</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.6182" target="_blank" >10.1002/mma.6182</a>
Alternative languages
Result language
angličtina
Original language name
Curvature driven flow of a family of interacting curves with applications
Original language description
In this paper, we investigate a system of geometric evolution equations describing a curvature-driven motion of a family of planar curves with mutual interactions that can have local as well as nonlocal character, and the entire curve may influence evolution of other curves. We propose a direct Lagrangian approach for solving such a geometric flow of interacting curves. We prove local existence, uniqueness, and continuation of classical Hölder smooth solutions to the governing system of nonlinear parabolic equations. A numerical solution to the governing system has been constructed by means of the method of flowing finite volumes. We also discuss various applications of the motion of interacting curves arising in nonlocal geometric flows of curves as well as an interesting physical problem of motion of two interacting dislocation loops in the material science.
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
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Methods in the Applied Sciences
ISSN
0170-4214
e-ISSN
1099-1476
Volume of the periodical
43
Issue of the periodical within the volume
7
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
4177-4190
UT code for WoS article
000508314200001
EID of the result in the Scopus database
2-s2.0-85078812584