On the Hedstrom nonreflecting boundary condition for C2C2 solutions

This paper shows that Hedstrom's nonreflecting boundary condition works for some nonsimple-wave solutions in the case where the solution is C2C2. Hedstrom's 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 Hedstrom's theorem for C2C2 solutions, that is, we prove that the Hedstrom boundary condition eliminates the reflection if the solution is C2C2 and there do not exist ingoing waves generated by the nonlinear interactions near the boundary.