American Institute of Mathematical Sciences

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2013, 2013(special): 791-796. doi: 10.3934/proc.2013.2013.791

Schrödinger equation with noise on the boundary

Frank Wusterhausen 1,

1. 

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

Received  August 2012 Published  November 2013

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: Dirichlet noise, Neumann noise, stochastic partial differential equations., Schrödinger Equation.
Mathematics Subject Classification: Primary: 60H15; Secondary: 35G16, 35Q4.
Citation: Frank Wusterhausen. Schrödinger equation with noise on the boundary. Conference Publications, 2013, 2013 (special) : 791-796. doi: 10.3934/proc.2013.2013.791
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.

show all references

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.

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