Curvature driven flow of a family of interacting curves with applications

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Curvature driven flow of a family of interacting curves with applications

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Curvature driven flow of a family of interacting curves with applications

Popis výsledku anglicky

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.

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%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Mathematical Methods in the Applied Sciences

ISSN

0170-4214

e-ISSN

1099-1476

Svazek periodika

43

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

4177-4190

Kód UT WoS článku

000508314200001

EID výsledku v databázi Scopus

2-s2.0-85078812584