Operator estimates for non-periodically perforated domains: disappearance of cavities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F24%3A50020478" target="_blank" >RIV/62690094:18470/24:50020478 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/full/10.1080/00036811.2023.2209726" target="_blank" >https://www.tandfonline.com/doi/full/10.1080/00036811.2023.2209726</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00036811.2023.2209726" target="_blank" >10.1080/00036811.2023.2209726</a>

Result language
angličtina
Original language name
Operator estimates for non-periodically perforated domains: disappearance of cavities
Original language description
We consider a boundary value problem for a general second-order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions on the shapes of the cavities and no condi-tions on their distribution in the domain. On the boundaries of the cavities, a nonlinear Robin condition is imposed. The sizes of the cavities and the minimal distance between them are supposed to satisfy a certain simple condition ensuring that under the homogenization the cavities disappear and we obtain a similar problem in a non-perforated domain. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in W-2(1)- and L-2-norms uniformly in L-2-norm of the right-hand side in the equation and provide the estimates for the convergence rates.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA22-18739S" target="_blank" >GA22-18739S: Asymptotic and spectral analysis of operators in mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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