KFU. Card publication. Nonlinear mixed Cherepanov boundary value problem

KAZAN
FEDERAL UNIVERSITY

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NONLINEAR MIXED CHEREPANOV BOUNDARY VALUE PROBLEM

Form of presentation

Articles in international journals and collections

Year of publication

2019

Язык

английский

Authors, employees of KFU

Obnosov Yuriy Viktorovich, author

Authors, postgraduates KFU

Zulkarnyaev Ayrat Rinatovich, postgraduate kfu

Bibliographic description in the original language

Obnosov Yurii, Zulkarnyaev Airat. Nonlinear mixed Cherepanov boundary value problem. Complex Variables and Elliptic Equations. V.64(6) 2019,p.979-996. DOI:10.1080/17476933.2018.1493465

Annotation

We consider the nonlinear boundary-value problem, consisting in the determination of the function $w(z)$ which is meromorphic in the upper half-plane, satisfies the homogeneous Hilbert boundary condition on the set $L$ of $n$ intervals of the real axis, and has the given modulus on the set $M={\mathbb R}\setminus \overline L$. This problem was set and solved in \cite{cherepanov1}. G.P.Cherepanov proved that the required solution with a given number and location of its internal zeros and poles and with integrable singularities at all endpoints of $L$ exists if and only if $n-1$ solvability conditions are fulfilled. Our goal is to prove that this problem is unconditionally solvable in the class of meromorphic functions with properly chosen number and location of their zeros and poles. We show that the formulated problem is equivalent to the real analog of the Jacobi inversion problem on a hyperelliptic Riemann surface. The general meromorphic solution is obtained as well as the solut

Keywords

nonlinear mixed boundary-value problem, analytic functions, closed form solution

The name of the journal

Complex Variables and Elliptic Equations

URL

http://10.1080/17476933.2018.1493465

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

https://repository.kpfu.ru/eng/?p_id=184241&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Obnosov Yuriy Viktorovich	ru_RU
dc.contributor.author	Zulkarnyaev Ayrat Rinatovich	ru_RU
dc.date.accessioned	2019-01-01T00:00:00Z	ru_RU
dc.date.available	2019-01-01T00:00:00Z	ru_RU
dc.date.issued	2019	ru_RU
dc.identifier.citation	Obnosov Yurii, Zulkarnyaev Airat. Nonlinear mixed Cherepanov boundary value problem. Complex Variables and Elliptic Equations. V.64(6) 2019,p.979-996. DOI:10.1080/17476933.2018.1493465	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=184241&p_lang=2	ru_RU
dc.description.abstract	Complex Variables and Elliptic Equations	ru_RU
dc.description.abstract	We consider the nonlinear boundary-value problem, consisting in the determination of the function $w(z)$ which is meromorphic in the upper half-plane, satisfies the homogeneous Hilbert boundary condition on the set $L$ of $n$ intervals of the real axis, and has the given modulus on the set $M={\mathbb R}\setminus \overline L$. This problem was set and solved in \cite{cherepanov1}. G.P.Cherepanov proved that the required solution with a given number and location of its internal zeros and poles and with integrable singularities at all endpoints of $L$ exists if and only if $n-1$ solvability conditions are fulfilled. Our goal is to prove that this problem is unconditionally solvable in the class of meromorphic functions with properly chosen number and location of their zeros and poles. We show that the formulated problem is equivalent to the real analog of the Jacobi inversion problem on a hyperelliptic Riemann surface. The general meromorphic solution is obtained as well as the solut	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	nonlinear mixed boundary-value problem	ru_RU
dc.subject	analytic functions	ru_RU
dc.subject	closed form solution	ru_RU
dc.title	Nonlinear mixed Cherepanov boundary value problem	ru_RU
dc.type	Articles in international journals and collections	ru_RU