Examples



mdbootstrap.com



 
Статья
2013

On a weighted boundary-value problem in an infinite half-strip for a biaxisymmetric Helmholtz equation


A. A. AbashkinA. A. Abashkin
Русская математика
https://doi.org/10.3103/S1066369X13060017
Abstract / Full Text

We study a boundary-value problem for a generalized biaxisymmetric Helmholtz equation. Boundary conditions in this problem depend on equation parameters. By the method of separation of variables, using the Fourier-Bessel series expansion and the Hankel transform, we prove the unique solvability of the problem and establish explicit formulas for its solution.

Author information
  • Samara State University of Architecture and Civil Engineering, ul. Molodogvardeiskaya 194, Samara, 443001, RussiaA. A. Abashkin
References
  1. O. I. Marichev, A. A. Kilbas, and O.A. Repin, Boundary-Value Problems for Partial Differential Equations with Discontinuous Coefficients (CGEU, Samara, 2008) [in Russian].
  2. M.E. Lerner and O. A. Repin, “The Dirichlet Problem for the Generalized Biaxisymmetric Helmholtz Equation in the First Quadrant,” Vestn. Samarsk. Gos. Tekhn. Univ. 6, 5–8 (1998).
  3. M. E. Lerner and O. A. Repin, “Nonlocal Boundary-Value Problems in a Vertical Half-Strip for the Generalized Axisymmetric Helmholtz Equation,” Differents. Uravneniya 37, 1640–1642 (2001).
  4. E. I. Moiseev, “On the Solvability of a Nonlocal Boundary-Value Problem,” Differents. Uravneniya 37, 1643–1646 (2001).
  5. E. V. Shimkovich, “Weighted Boundary-Value Problems for a Degenerate Equation of Elliptic Type in a Half-Strip,” Litovskii Matem. Sborn. 30, 185–196 (1990).
  6. M. Kh. Ruziev, “The Dirichlet Problem in a Vertical Half-Strip for a Degenerated Elliptic Equation with a Singular Coefficient and Spectral Parameter,” in Proceedings of Conference “Differential Equations, Theory of Functions, and Applications” (Novosibirsk, 2007), pp. 268–269.
  7. N. N. Lebedev, Special Functions and Their Applications (Lan’, Saint-Petersburg, 2010) [in Russian].