KFU. Card publication. Periodic Boundary Value Problem for a Linear Elliptic Equation of the Second Order in a Half-Plane

KAZAN
FEDERAL UNIVERSITY

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PERIODIC BOUNDARY VALUE PROBLEM FOR A LINEAR ELLIPTIC EQUATION OF THE SECOND ORDER IN A HALF-PLANE

Form of presentation

Articles in international journals and collections

Year of publication

2020

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Authors, employees of KFU

Bikchantaev Ildar Akhmedovich, author

Bibliographic description in the original language

I.A. Bikchantaev. Periodic Boundary Value Problem for a Linear Elliptic Equation of the Second Order in a Half-Plane. Differential Equations, 2020, Vol. 56, No. 7, pp. 813–818.

Annotation

We study periodic boundary value problems for a second-order linear partial differ- ential equation with constant coefficients in a half-plane under various assumptions about the roots of the characteristic equation. If the imaginary parts of these roots are of the same sign, then we consider a boundary value problem of the type of the Hilbert problem, and if they are of opposite signs, then we consider a problem of the Dirichlet type. Necessary and sufficient solv- ability conditions are obtained, explicit formulas are given for the solutions of these problems, and the number of solutions of the corresponding homogeneous problems is found.

Keywords

boundary value problem, elliptic equation

The name of the journal

Differential Equations

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=237056&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchantaev Ildar Akhmedovich	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	I.A. Bikchantaev. Periodic Boundary Value Problem for a Linear Elliptic Equation of the Second Order in a Half-Plane. Differential Equations, 2020, Vol. 56, No. 7, pp. 813–818.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=237056&p_lang=2	ru_RU
dc.description.abstract	Differential Equations	ru_RU
dc.description.abstract	We study periodic boundary value problems for a second-order linear partial differ- ential equation with constant coefficients in a half-plane under various assumptions about the roots of the characteristic equation. If the imaginary parts of these roots are of the same sign, then we consider a boundary value problem of the type of the Hilbert problem, and if they are of opposite signs, then we consider a problem of the Dirichlet type. Necessary and sufficient solv- ability conditions are obtained, explicit formulas are given for the solutions of these problems, and the number of solutions of the corresponding homogeneous problems is found.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	boundary value problem	ru_RU
dc.subject	elliptic equation	ru_RU
dc.title	Periodic Boundary Value Problem for a Linear Elliptic Equation of the Second Order in a Half-Plane	ru_RU
dc.type	Articles in international journals and collections	ru_RU