The Riemann-Green function and the invariant imbedding equations for hyperbolic systems of first-order1

摘要

In the present paper we deal with a boundary value problem for a hyperbolic system of first-order in one space variable. An explicit integral representation for the Riemann-Green function is first obtained, from which a set of discontinuities at both the initial time and along certain characteristics are calculated next. The reflection and transmission functions are then defined by simply evaluating this function at certain boundary points, and finally, a set of integro/partial differential equations satisfied by the reflection and transmission functions is derived. There are the time-dependent invariant imbedding equations for the systems we consider here, and these extend the results obtained by Corones and Krueger for second-order hyperbolic equations.