Martin-Luther-Universität Halle-Wittenberg

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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.

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