QUALITATIVE AND NUMERICAL ASPECTS OF A MOTION OF A FAMILY OF INTERACTING CURVES IN SPACE
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00364257" target="_blank" >RIV/68407700:21340/22:00364257 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1137/21M1417181" target="_blank" >https://doi.org/10.1137/21M1417181</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1417181" target="_blank" >10.1137/21M1417181</a>
Alternative languages
Result language
angličtina
Original language name
QUALITATIVE AND NUMERICAL ASPECTS OF A MOTION OF A FAMILY OF INTERACTING CURVES IN SPACE
Original language description
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of three-dimensional curves in the normal and binormal directions. Evolving curves may be the subject of mutual interactions having both local or nonlocal character where the entire curve may influence evolution of other curves. Such an evolution and interaction can be found in applications. We explore the direct Lagrangian approach for treating the geometric flow of such interacting curves. Using the abstract theory of nonlinear analytic semiflows, we are able to prove local existence, uniqueness, and continuation of classical Ho"lder smooth solutions to the governing system of nonlinear parabolic equations. Using the finite volume method, we construct an efficient numerical scheme solving the governing system of nonlinear parabolic equations. Additionally, a nontrivial tangential velocity is considered allowing for redistribution of discretization nodes. We also present several computational studies of the flow combining the normal and binormal velocity and considering nonlocal interactions.
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%2F0000753" target="_blank" >EF16_019/0000753: Research centre for low-carbon energy technologies</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN
0036-1399
e-ISSN
1095-712X
Volume of the periodical
82
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
549-575
UT code for WoS article
000803935500007
EID of the result in the Scopus database
2-s2.0-85130685715