A nonlocal problem for mixed type equation with singular coefficient in domain with half-strip as hyperbolic part

Abstract

A nonlocal problem for mixed type equation with a singular coefficient and the spectral parameter is formulated in the field, which hyperbolic part is vertical half-strip and elliptic part is rectangle. The nonlocal condition of problem combines the values of required function on the right and left boundaries of half-stripe and rectangle. The only requirement on the unknown function in the change type line is continuity. To research the given problem we apply the spectral method. The uniqueness and existence of a solution are proved. The solution is constructed as biortogonal series. Coefficients of this series should require special ODE systems, solved in the paper. The uniform convergence of the series is proved with the restrictions on problem conditions.

Keywords

• mixed type equation
• equation with a singular coefficient
• biorthogonal series
• riesz basis
• bessel functions