A problem with an analog of Frankl condition on the characteristics for gellerstedt equation with singular coefficient

We investigate the problem with an analog of Frankl condition on boundary characteristics for generalized Tricomi equation. We prove that the formulated problem is correct.     

A problem with a nonlocal boundary condition on the characteristic for a class of equations of mixed type

We study the boundary-value problem with a nonlocal boundary condition on the characteristic for a class of equations of mixed type. The unique solvability of the problem is proved.     

A boundary value problem for a class of mixed-type equations in an unbounded domain

We consider a boundary value problem for an equation of the mixed type with a singular coefficient in an unbounded domain. The uniqueness of the solution of the problem is proved with the use of the extremum principle. In the proof of the existence of a solution of the problem, we use the method of integral equations.     

Problem with Frankl and Bitsadze-Samarskii conditions on the degeneration line and on parallel characteristics for the gellerstedt equation with a singular coefficient

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.     

On a problem with a shift and with the Frankl condition on a segment of the degeneration line for a class of equations of mixed type

We consider the Frankl-Nakhushev problem. By using the maximum principle, we prove the uniqueness of the solution of the problem in the class of Hölder functions, and by using the method of integral equations, in particular, the recently developed method of Wiener-Hopf equations, we prove its existence.     

Tricomi-Nakhushev problem

In the Tricomi problem, the values of the unknown function are given at all points of a characteristic. We study the well-posedness of a problem in which part of the characteristic is free of the boundary condition and the lacking Tricomi condition is equivalently replaced by A.M. Nakhushev’s nonlocal condition with shift.     

Problem with shift on parallel characteristics for Gellerstedt equation with singular coefficient

We study correctness for a problemwith an analog of Frankl condition on a degeneration line segment and dislocation conditions on parallel characteristics for Gellerstedt equation with singular coefficient. With the help of maximum principle we prove uniqueness of a solution to the problem and with the method of integral equations we prove the existence of a solution to the problem.     

A nonlocal boundary-value problem for the gellerstedt equation

We consider the boundary-value problem for the Gellerstedt equation