Problem with Frankl and Bitsadze-Samarskii conditions on the degeneration line and on parallel characteristics for the gellerstedt equation with a singular coefficient
М. МирсабуровTermez State University, Termez, UzbekistanU. E. BobomurodovTermez State University, Termez, Uzbekistan
ABI
Abstract
We study the well-posedness of a problem for the Gellerstedt equation with a singular coefficient and with the Frankl and Bitsadze-Samarskii conditions on the degeneration line and on parallel characteristics. The uniqueness of the solution of the considered problem is proved with the use of the extremum principle, and the existence of the solution of the problem is justified with the use of the theories of singular integral equations, Wiener-Hopf equations, and Fredholm integral equations.