POLYNOMIAL SOLUTIONS TO THE MIXED DIRICHLET-NEUMANN BOUNDARY VALUE PROBLEM FOR THE TRICOMI EQUATION IN THE STRIP

Abstract

An inhomogeneous Tricomi equation is considered in a strip with a polynomial right-hand side. It is shown that the Dirichlet-Neumann boundary value problem with polynomial boundary conditions has a polynomial solution. An algorithm for constructing this polynomial solution is presented and examples are considered. If the strip lies in the ellipticity region of the equation, then this solution is unique in the class of functions of polynomial growth. If the strip lies in a mixed region, then the solution to the Dirichlet-Neumann problem is not unique in the class of functions of polynomial growth, but it is unique in the class of polynomials.