DEZIN NONLOCAL PROBLEM FOR A MIXED-TYPE EQUATION WITH POWER DEGENERATION


Cite item

Abstract

In this article, for the equation of mixed elliptic - hyperbolic type with a power degeneracy on the transition line in a rectangular area are studied the problem Dezin with periodicity conditions and non-local condition, binding values of the normal derivative on the lower base of the rectangle with the value of the target solution on the line type of study. Necessary and sufficient conditions for the uniqueness of the solution were settled, and the uniqueness of the solution was proved problem on the based on completeness of the system of peculiar functions of one-problem or the peculiar.

About the authors

V. A. Gushchina

Department of Math, Volga region socially-humanitarian academy, 55/57 Maxim Gorky str., Samara, 443090, Russian Federation.

Author for correspondence.
Email: morenov.sv@ssau.ru

References

  1. Dezin A.A. On the solvable extensions of partial differential operators. Outlines of the Joint Soviet — American Symposium on Partial Differential Equations, 1963. Novosibirsk, pp. 65–66 .
  2. Dezin A.A. Operators of the first time derivative and nonlocal boundary conditions. Proceedings AN of SSSR, 1967, Vol. 31, no. 1, pp. 61–86 .
  3. Nahushev A.M. Problems with shift for partial differential equations. M.: Nauka, 2006, 287 p. .
  4. Nakhusheva Z.A. A nonlocal problem A.A. Dezin for the Lavrent’ev-Bitsadze equation. Differents. Equation, 2009, Vol. 45, no. 8, pp. 1199–2003 .
  5. Nakhusheva ZA Non-local boundary value problems for the major and mixed types of differential equations (Publ KBSC RAS, Nalchik — 2011) .
  6. Sabitov K.B., Novikova V.A. A nonlocal problem A.A. Dezin for the Lavrent’ev — Bitsadze’s equation. Proceedings of universities, 2016, Vol. 6, pp. 61–72 .
  7. Sabitov K.B., Gushina (Novikova) V.A. The Dezin’s problem for inhomogeneous Lavrent’ev - Bitsadze’s equation. Proceedings of universities (accepted for publication) .
  8. Sabitov K.B. Dirichlet problem for equations of mixed type in rectangular area. Report RAN. 2007, Vol. 413, no. 1, pp. 23–26 .
  9. Sabitov K.B., Sidorenko O.G. The problem with periodicity conditions for a mixed-type degenerate equation. Differential equations, 2010, Vol. 46, no. 1, pp. 105–113 .
  10. Sabitov K.B., Vagapova E.V. The Dirichlet is problem for an equation of mixed type with two lines of degeneracy in a rectangular area. Differential equations, 2013, Vol. 49, no. 1, pp. 68–78 .
  11. Sabitov K.B. Equations of mathematical physics. M.: FIZMATLIT. 2003. 352 p.

Copyright (c) 2017 В. А. Гущина

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies