Asymptotic behaviour of the scattering phase for non-trapping obstacles
Let be the scattering matrix related to the wave equation in the exterior of a non-trapping obstacle , with Dirichlet or Neumann boundary conditions on . The function , called scattering phase, is determined from the equality . We show that has an asymptotic expansion as and we compute the first three coefficients. Our result proves the conjecture of Majda and Ralston for non-trapping obstacles.