Schrödinger equation with noise on the boundary

Pages: 791 - 796, Issue special, November 2013

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Frank Wusterhausen - Martin-Luther-Universität, Halle-Wittenberg, Institute of Mathematics, 06099 Halle (Saale), Germany (email)

Abstract: We treat the question of existence and uniqueness of distributional solutions for the linear Schrödinger equation in a bounded domain with boundary noise. We cover both Dirichlet and Neumann noise. For the proof we make use of spectral decomposition of the Laplacian with homogeneous Neumann/Direchlet boundary condition.

Keywords:  Neumann noise, Dirichlet noise, Schrödinger Equation, stochastic partial differential equations.
Mathematics Subject Classification:  Primary: 60H15; Secondary: 35G16, 35Q41.

Received: August 2012; Published: November 2013.