30. November
Maximilian Klumpp (Uni Stuttgart)
Schrödinger approximation for the Helmholtz equation
Abstract:
Time-harmonic electromagnetic waves in vacuum are described by the Helmholtz equation ∆u + ω^2 u = 0 for (x, y, z) ∈ R^3 . For the evolution of such waves along the z-axis a Schrödinger equation can be derived through a multiple scaling ansatz. This formal approximation can be justified by proving bounds between this formal approximation and true solutions of the original system. The challenge here is the fact that the Helmholtz equation is ill-posed as an evolutionary system along the z-axis.