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: August 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

[1]	H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in "Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992)" (eds. H.-J. Schmeisser), Teubner-Texte Math., 133, Teubner, Stuttgart (1993), 9-126.
[2]	G. Da Prato and J. Zabczyk, Evolution equations with white-noise boundary conditions, Stochastics Stochastics Rep. 42 (1993), 167-182.
[3]	I. Lasiecka and R. Triggiani, "Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory" Lecture Notes in Control and Information Sciences, 164. Springer-Verlag, Berlin, 1991.
[4]	J.-L. Lions and E. Magenes, "Non-homogeneous boundary value problems and applications. Vol. I.," Translated from the French by P. Kenneth. Die Grundlehren der mathematischen Wissenschaften, Band 181. Springer-Verlag, New York-Heidelberg, 1972.