Abstract:
As part of this scientific work, we study a displacement boundary value problem for a third-order parabolichyperbolic
type equation with a third-order parabolic equation backward in time and a wave equation in
the domain of hyperbolicity. As one of the boundary conditions we have a linear combination including
variable coefficients of the sought function on the characteristic lines AC and BC. The present paper
reports following results: inequality between characteristics of AC and BC lines limiting the hyperbolic
part
1 of the domain
as carriers of data for the Tricomi problem as 0 x 2 , as a matter of fact, the
solvability of the Tricomi problem with data on the characteristic line BC does not imply the solvability
of the Tricomi problem with data on the AC; necessary and sufficient conditions for the existence and
uniqueness of a regular solution to the problem under study are found. Under certain conditions for the
given functions, the solution to the problem under study is written out explicitly. It is shown that under
violation of the necessary conditions established in this paper the homogeneous problem has innumerable
linearly independent solutions, while the set of solutions to the corresponding inhomogeneous problem can
exist only with additional conditions.
