Казанский (Приволжский) федеральный университет, КФУ
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NONLINEAR MIXED CHEREPANOV BOUNDARY VALUE PROBLEM
Форма представленияСтатьи в зарубежных журналах и сборниках
Год публикации2019
Языканглийский
  • Обносов Юрий Викторович, автор
  • Зулькарняев Айрат Ринатович, автор
  • Библиографическое описание на языке оригинала 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
    Аннотация 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
    Ключевые слова nonlinear mixed boundary-value problem, analytic functions, closed form solution
    Название журнала Complex Variables and Elliptic Equations
    URL http://10.1080/17476933.2018.1493465
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