Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021095" target="_blank" >RIV/62690094:18470/23:50021095 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1134/S0081543823030057" target="_blank" >https://doi.org/10.1134/S0081543823030057</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1134/S0081543823030057" target="_blank" >10.1134/S0081543823030057</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition

Popis výsledku v původním jazyce

A two-dimensional boundary value problem is studied for a general scalar elliptic second-order equation of the general form with frequent alternation of boundary conditions. The alternation is defined on small, closely spaced parts of the boundary on which the Dirichlet boundary condition and the nonlinear Robin boundary condition are set alternately. The distribution and size of these segments are arbitrary. The case is considered when, upon homogenization, the Dirichlet boundary condition completely disappears and only the original nonlinear Robin boundary condition remains. The main result is estimates for the W-2(1)- and L-2-norms of the difference between the solutions of the perturbed and homogenized problems, which are uniform in the L-2-normof the right-hand side and characterize the rate of convergence. It is shown that these estimates are order sharp.

Název v anglickém jazyce

Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition

Popis výsledku anglicky

A two-dimensional boundary value problem is studied for a general scalar elliptic second-order equation of the general form with frequent alternation of boundary conditions. The alternation is defined on small, closely spaced parts of the boundary on which the Dirichlet boundary condition and the nonlinear Robin boundary condition are set alternately. The distribution and size of these segments are arbitrary. The case is considered when, upon homogenization, the Dirichlet boundary condition completely disappears and only the original nonlinear Robin boundary condition remains. The main result is estimates for the W-2(1)- and L-2-norms of the difference between the solutions of the perturbed and homogenized problems, which are uniform in the L-2-normof the right-hand side and characterize the rate of convergence. It is shown that these estimates are order sharp.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotická a spektrální analýza operátorů v matematické fyzice</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Steklov Institute of Mathematics

ISSN

0081-5438

e-ISSN

1531-8605

Svazek periodika

321

Číslo periodika v rámci svazku

SUPPL 1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

"S33"-"S52"

Kód UT WoS článku

001073881600004

EID výsledku v databázi Scopus

2-s2.0-85171379977