QUALITATIVE AND NUMERICAL ASPECTS OF A MOTION OF A FAMILY OF INTERACTING CURVES IN SPACE

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

QUALITATIVE AND NUMERICAL ASPECTS OF A MOTION OF A FAMILY OF INTERACTING CURVES IN SPACE

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

QUALITATIVE AND NUMERICAL ASPECTS OF A MOTION OF A FAMILY OF INTERACTING CURVES IN SPACE

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000753" target="_blank" >EF16_019/0000753: Centrum výzkumu nízkouhlíkových energetických technologií</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM JOURNAL ON APPLIED MATHEMATICS

ISSN

0036-1399

e-ISSN

1095-712X

Svazek periodika

82

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

549-575

Kód UT WoS článku

000803935500007

EID výsledku v databázi Scopus

2-s2.0-85130685715