Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip
Analysis of PDEs
2018-07-13 v1 Mathematical Physics
math.MP
Abstract
An inhomogeneous Tricomi equation is considered in a strip with a polynomial right-hand side. It is shown that the Dirichlet boundary value problem with polynomial boundary conditions has a polynomial solution. An algorithm for constructing this polynomial solution is given 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 of the Dirichlet problem is not unique in the class of functions of polynomial growth, but it is unique in the class of polynomials.
Keywords
Cite
@article{arxiv.1807.04627,
title = {Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip},
author = {Oleg D. Algazin},
journal= {arXiv preprint arXiv:1807.04627},
year = {2018}
}