Transmission problem for the Laplace equation and the integral equation method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00370680" target="_blank" >RIV/67985840:_____/12:00370680 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2011.09.041" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2011.09.041</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2011.09.041" target="_blank" >10.1016/j.jmaa.2011.09.041</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Transmission problem for the Laplace equation and the integral equation method

Popis výsledku v původním jazyce

We shall study a weak solution in the Sobolev space of the transmission problem for the Laplace equation using the integral equation method. First we use the indirect integral equation method. We look for a solution in the form of the sum of the double layer potential corresponding to the skip of traces on the interface and a single layer potential with an unknown density. We get an integral equation on the boundary. We prove that this equation has a form (I + M)phi = F where M is a contractive operator. So, we can obtain a solution of this equation using the successive approximation method. Moreover, we are able to estimate the norm of the operator M and control how quickly this process converges. Then we study the direct integral equation method. Weobtain the same integral equation like for the indirect integral equation method. So, we can again calculate a solution using the successive approximation method.

Název v anglickém jazyce

Transmission problem for the Laplace equation and the integral equation method

Popis výsledku anglicky

We shall study a weak solution in the Sobolev space of the transmission problem for the Laplace equation using the integral equation method. First we use the indirect integral equation method. We look for a solution in the form of the sum of the double layer potential corresponding to the skip of traces on the interface and a single layer potential with an unknown density. We get an integral equation on the boundary. We prove that this equation has a form (I + M)phi = F where M is a contractive operator. So, we can obtain a solution of this equation using the successive approximation method. Moreover, we are able to estimate the norm of the operator M and control how quickly this process converges. Then we study the direct integral equation method. Weobtain the same integral equation like for the indirect integral equation method. So, we can again calculate a solution using the successive approximation method.

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

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

387

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

7

Strana od-do

837-843

Kód UT WoS článku

000297229900031

EID výsledku v databázi Scopus

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