Experimental Mathematics

Experimental Study of the HUM Control Operator for Linear Waves

Gilles Lebeau and Maëlle Nodet

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Abstract

We consider the problem of the numerical approximation of the linear controllability of waves. All our experiments are done in a bounded domain $\Omega$ of the plane, with Dirichlet boundary conditions and internal control. We use a Galerkin approximation of the optimal control operator of the continuous model, based on the spectral theory of the Laplace operator in $\Omega$. This allows us to obtain surprisingly good illustrations of the main theoretical results available on the controllability of waves and to formulate some questions for future analysis of the optimal control theory of waves.

Article information

Source
Experiment. Math., Volume 19, Issue 1 (2010), 93-120.

Dates
First available in Project Euclid: 12 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.em/1268404805

Mathematical Reviews number (MathSciNet)
MR2649987

Zentralblatt MATH identifier
1190.35011

Subjects
Primary: 35B37 65-05: Experimental papers 35L05: Wave equation 35A27: Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]

Keywords
Partial differential equations optimal control experimental mathematics numerical analysis microlocal analysis

Citation

Lebeau, Gilles; Nodet, Maëlle. Experimental Study of the HUM Control Operator for Linear Waves. Experiment. Math. 19 (2010), no. 1, 93--120. https://projecteuclid.org/euclid.em/1268404805


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