On the Hedstrom nonreflecting boundary condition for solutions

This paper shows that Hedstromʹs nonreflecting boundary condition works for some nonsimple-wave solutions in the case where the solution is C 2 . Hedstromʹs boundary condition is a pioneering work in the discipline of characteristic nonreflecting boundary conditions and Hedstrom gave a theoretical assurance of the nonreflectivity for simple-wave solutions. In this paper, we extend Hedstromʹs theorem for C 2 solutions, that is, we prove that the Hedstrom boundary condition eliminates the reflection if the solution is C 2 and there do not exist ingoing waves generated by the nonlinear interactions near the boundary.