Area preserving geodesic curvature driven flow of closed curves on a surface

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00316901" target="_blank" >RIV/68407700:21340/17:00316901 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14025" target="_blank" >http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14025</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/dcdsb.2017148" target="_blank" >10.3934/dcdsb.2017148</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Area preserving geodesic curvature driven flow of closed curves on a surface

Popis výsledku v původním jazyce

We investigate a non-local geometric flow preserving surface area enclosed by a curve on a given surface evolved in the normal direction by the geodesic curvature and the external force. We show how such a flow of surface curves can be projected into a flow of planar curves with the non-local normal velocity. We prove that the surface area preserving flow decreases the length of the evolved surface curves. Local existence and continuation of classical smooth solutions to the governing system of partial differential equations is analysed as well. Furthermore, we propose a numerical method of flowing finite volume for spatial discretization in combination with the Runge-Kutta method for solving the resulting system. Several computational examples demonstrate variety of evolution of surface curves and the order of convergence.

Název v anglickém jazyce

Area preserving geodesic curvature driven flow of closed curves on a surface

Popis výsledku anglicky

We investigate a non-local geometric flow preserving surface area enclosed by a curve on a given surface evolved in the normal direction by the geodesic curvature and the external force. We show how such a flow of surface curves can be projected into a flow of planar curves with the non-local normal velocity. We prove that the surface area preserving flow decreases the length of the evolved surface curves. Local existence and continuation of classical smooth solutions to the governing system of partial differential equations is analysed as well. Furthermore, we propose a numerical method of flowing finite volume for spatial discretization in combination with the Runge-Kutta method for solving the resulting system. Several computational examples demonstrate variety of evolution of surface curves and the order of convergence.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Discrete and Continuous Dynamical Systems - B

ISSN

1531-3492

e-ISSN

1553-524X

Svazek periodika

22

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

3671-3689

Kód UT WoS článku

000409969500004

EID výsledku v databázi Scopus

2-s2.0-85028714703