This article is cited in 1 paper

Solving one boundary-value problem for mixed type equation with two singular lines with the use of spectral method

A. A. Abashkin

Chair of Higher Mathematics, Samara State University of Architecture and Civil Engineering, 194 Molodogvardeyskaya str., Samara, 443001 Russia

Abstract: For mixed type equation with two perpendicular singularity lines, we consider one boundary problem in the domain whose elliptic and hyperbolic part is rectangle and vertical half-strip, respectively. This problem differs from the Dirichlet problem by the fact that at the left boundary of the rectangle and of half-strip we specify not the unknown function, but the order of zero. We prove uniqueness of boundary problem solution by a spectral method with the use of Fourier–Bessel series. We give substantiation of uniform convergence of corresponding series with some restrictions upon the conditions of the problem.

Keywords: mixed type equations, equation with singular coefficients, spectral method, Fourier–Bessel series, Bessel functions.

UDC: 517.956

Received: 23.07.2014
Revised: 13.10.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:2, 1–6

Bibliographic databases:

• 
•