Convergence of the Neumann series in BEM for the Neumann problem of the stokes system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00367466" target="_blank" >RIV/67985840:_____/11:00367466 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10440-011-9643-5" target="_blank" >http://dx.doi.org/10.1007/s10440-011-9643-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10440-011-9643-5" target="_blank" >10.1007/s10440-011-9643-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Convergence of the Neumann series in BEM for the Neumann problem of the stokes system

Popis výsledku v původním jazyce

A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability of the problem are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. Using boundary behavior of potentials we get an integral equation on the boundary of the domain where the trace of the velocity part of the solution is unknown.

Název v anglickém jazyce

Convergence of the Neumann series in BEM for the Neumann problem of the stokes system

Popis výsledku anglicky

A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability of the problem are given. Moreover, it is shown that we can obtain a solution of this integral equation using the successive approximation method. Then the consequences for the direct boundary integral equation method are treated. A solution of the Neumann problem for the Stokes system is the sum of the hydrodynamical single layer potential corresponding to the boundary condition and the hydrodynamical double layer potential corresponding to the trace of the velocity part of the solution. Using boundary behavior of potentials we get an integral equation on the boundary of the domain where the trace of the velocity part of the solution is unknown.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/IAA100190804" target="_blank" >IAA100190804: Pohyb tuhých těles v kapalinách: matematická analýza, numerická simulace a související problémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Acta Applicandae Mathematicae

ISSN

0167-8019

e-ISSN

—

Svazek periodika

116

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

281-304

Kód UT WoS článku

000300084300004

EID výsledku v databázi Scopus

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