A Mixed Problem for One 3D Space Analogue of Hyperbolic Type Equation

Abstract


It is well known that differential equations with an operator are used for study of the processes connected with appearances of vibration and other mechanics problems, and also play an essential role in the theory of approximation and mapping. In the present work a unique solution for the mixed problem of the full hyperbolic equation of the third order with constant factors, in a three-dimensional Euclidean space, was obtain with the Riemann method, which then becomes considerably simpler at the expense of integral representation of one of boundary conditions. Owing to this it can be used for statement and a solution of new boundary value problems.

About the authors

Mikhail V Dolgopolov

Samara State University

Email: mikhaildolgopolov@rambler.ru
(к.ф.-м.н., доцент), доцент, зав. лаб., каф. общей и теоретической физики, научно-исследовательская лаборатория математической физики; Самарский государственный университет; Samara State University

Irina N Rodionova

Samara State University

(к.ф.-м.н., доцент), доцент, каф. математики и бизнес-информатики; Самарский государственный университет; Samara State University

References

  1. Долгополов В.М., Долгополов М.В., Родионова И.Н. Построение специальных классов решений некоторых дифференциальных уравнений гиперболического типа // ДАН. Математика, 2009. - Т. 429, №5. - С. 583-589; англ. пер.: Dolgopolov V. М., Dolgopo-lovM. V., Rodionoval. N. Construction of special classes of solutions for some differential equations of hyperbolic type// Dokl. Math., 2009. - Vol. 80, No. 3. - P. 860-866.
  2. Волкодавов В. Ф., Николаев Н.Я., Быстрова O.K., Захаров В.Н. Функции для некоторых дифференциальных уравнений в те-мерном евклидовом пространстве и их применение. - Самара: Самарский университет, 1995. - 75 с.

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