Cloaking via impedance boundary condition for the 2-D Helmholtz equation

We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study...

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Bibliographic Details
Published in:Applicable analysis 2014-02, Vol.93 (2), p.254-268
Main Author: Alekseev, G.V.
Format: Article
Language:English
Subjects:
Boundaries
Boundary conditions
boundary control
control problem
Control theory
Dirichlet problem
Functionals
Helmholtz equation
Helmholtz equations
Impedance
Mathematical functions
Mathematical problems
mixed boundary value problem
Optimization
Partial differential equations
Perturbation methods
solvability
stability estimates
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Summary:We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study is played by boundary impedance. Quadratic tracking-type functionals for the field play the role of cost functionals. Solvability of control problems is proved. The uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2013.768340