Schrödinger equation with noise on the boundary

Frank Wusterhausen

doi:10.3934/proc.2013.2013.791

Article Contents

2013, Volume 2013: 791-796. Doi: 10.3934/proc.2013.2013.791 open access

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Schrödinger equation with noise on the boundary

Frank Wusterhausen^1,

1.
Martin-Luther-Universität, Halle-Wittenberg, Institute of Mathematics, 06099 Halle (Saale)

Received: July 31, 2012

Published: October 2013

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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.

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References

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