Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021222" target="_blank" >RIV/62690094:18470/23:50021222 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s10958-023-06893-1" target="_blank" >https://link.springer.com/article/10.1007/s10958-023-06893-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10958-023-06893-1" target="_blank" >10.1007/s10958-023-06893-1</a>

Result language

angličtina

Original language name

Asymptotic Analysis of Boundary-Value Problems for the Laplace Operator with Frequently Alternating Type of Boundary Conditions

Original language description

This work, which can be considered as a small monograph, is devoted to the study of two-and three-dimensional boundary-value problems for eigenvalues of the Laplace operator with frequently alternating type of boundary conditions. The main goal is to construct asymptotic expansions of the eigenvalues and eigenfunctions of the considered problems. Asymptotic expansions are constructed on the basis of original combinations of asymptotic analysis methods: the method of compatibility of asymptotic expansions, the boundary layer method, and the multiscale method. We perform the analysis of the coefficients of the formally constructed asymptotic series. For strictly periodic and locally periodic alternation of the boundary conditions, the described approach allows one to construct complete asymptotic expansions of the eigenvalues and eigenfunctions. In the case of nonperiodic alternation and the averaged third boundary condition, sufficiently weak conditions on the alternation structure are obtained, under which it is possible to construct the first corrections in the asymptotics for the eigenvalues and eigenfunctions. These conditions include in consideration a wide class of different cases of nonperiodic alternation. With further, very essential weakening of the conditions on the structure of alternation, it is possible to obtain two-sided estimates for the rate of convergence of the eigenvalues of the perturbed problem. It is shown that these estimates are unimprovable in order. For the corresponding eigenfunctions, we also obtain unimprovable in order estimates for the rate of convergence. © 2023, Springer Nature Switzerland AG.

Czech name

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Czech description

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Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

Journal of mathematical sciences

ISSN

1072-3374

e-ISSN

1573-8795

Volume of the periodical

277

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

118

Pages from-to

841-958

UT code for WoS article

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EID of the result in the Scopus database

2-s2.0-85180665503