KFU. Card publication. Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients

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PERIODIC CONJUGATION PROBLEM FOR LINEAR ELLIPTIC EQUATIONS OF SECOND ORDER WITH CONSTANT COEFFICIENTS

Form of presentation

Articles in Russian journals and collections

Year of publication

2018

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Authors, employees of KFU

Bikchantaev Ildar Akhmedovich, author

Bibliographic description in the original language

Bikchantaev I.A. Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients// Lobachevskii Journal of Mathematics - 2018 - Vol. 39 - No. 2, pp. 165-168.

Annotation

We consider a periodic problem of conjugation on the real axis for a linear differential elliptic equation of second order with constant coefficients. There is known a representation of general solution of the equation in terms of analytic functions depending on affine connected variables. We introduce auxiliary analytic functions enabling us to reduce the problem to a system of two periodic Riemann boundary value problems. That problem was solved first by L.I. Chibricova. We use her results for solving of our problem. We obtain its explicit solution and conditions of solvability, evaluate the index and defect numbers. We know a number of recent works dealing with periodic boundary value problems for elliptic linear differential equations. This subject is closely connected with the main equations of plane anisotropic theory of elasticity (see, for instanse, \cite{Wang}, \cite{HanWang}). In the present paper we research a boundary value problem of conjugation for elliptic equation.

Keywords

elliptic equation, boundary value problem, defect number, index, periodic solution

The name of the journal

Lobachevskii Journal of Mathematics

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

https://repository.kpfu.ru/eng/?p_id=176008&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchantaev Ildar Akhmedovich	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Bikchantaev I.A. Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients// Lobachevskii Journal of Mathematics - 2018 - Vol. 39 - No. 2, pp. 165-168.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=176008&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	We consider a periodic problem of conjugation on the real axis for a linear differential elliptic equation of second order with constant coefficients. There is known a representation of general solution of the equation in terms of analytic functions depending on affine connected variables. We introduce auxiliary analytic functions enabling us to reduce the problem to a system of two periodic Riemann boundary value problems. That problem was solved first by L.I. Chibricova. We use her results for solving of our problem. We obtain its explicit solution and conditions of solvability, evaluate the index and defect numbers. We know a number of recent works dealing with periodic boundary value problems for elliptic linear differential equations. This subject is closely connected with the main equations of plane anisotropic theory of elasticity (see, for instanse, \cite{Wang}, \cite{HanWang}). In the present paper we research a boundary value problem of conjugation for elliptic equation.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	elliptic equation	ru_RU
dc.subject	boundary value problem	ru_RU
dc.subject	defect number	ru_RU
dc.subject	index	ru_RU
dc.subject	periodic solution	ru_RU
dc.title	Periodic Conjugation Problem for Linear Elliptic Equations of Second Order with Constant Coefficients	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU