Differential and Integral Equations

Identification of boundary shape and reflectivity in a wave equation by optimal control techniques

Suzanne Lenhart, Vladimir Protopopescu, and Jiongmin Yong

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We apply optimal control techniques to find approximate solutions to an inverse problem for the acoustic wave equation. The inverse problem (assumed to have a unique solution) is to determine the shape and reflection coefficient of a part of the boundary from partial measurements of the acoustic signal. The sought functions are treated as controls and the goal - quantified by an objective functional - is to drive the model solution close to the experimental data by adjusting these functions. The problem is solved by finding the optimal control pair, which minimizes the objective functional. Then by driving the "cost of the control" to zero one proves that the sequence of optimal controls converges to the solution of the inverse problem.

Article information

Differential Integral Equations, Volume 13, Number 7-9 (2000), 941-972.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J20: Optimal control problems involving partial differential equations
Secondary: 35R30: Inverse problems 49K20: Problems involving partial differential equations 93B30: System identification


Lenhart, Suzanne; Protopopescu, Vladimir; Yong, Jiongmin. Identification of boundary shape and reflectivity in a wave equation by optimal control techniques. Differential Integral Equations 13 (2000), no. 7-9, 941--972. https://projecteuclid.org/euclid.die/1356061205

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