INTIAL BOUNDARY VALUE PROBLEM FOR THE LINEARIZED KDV EQUATION ON STAR GRAPH WITH ONE SEMI-INFINITE AND TWO BOUNDED BONDS

Abstract

In this article, we investigated an initial boundary value problem for the linearized KDV equation on a simple metric graph consisting of two bounded segments and one semi-infinite straight line connected at one point, called the vertex of the graph. The uniqueness of the solution is proved by the method of energy integrals.
Using the potential method, an integral formula is constructed for solving the problem under consideration.