Parameter identification for the linear wave equation with Robin boundary condition

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Code:
30/2017
Title:
Parameter identification for the linear wave equation with Robin boundary condition
Date:
Tuesday 20th June 2017
Author(s):
Bacchelli, V.; Micheletti, S.; Perotto, S.; Pierotti, D.
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Abstract:
We consider an initial-boundary value problem for the classical linear wave equation, where mixed boundary conditions of Dirichlet and Neumann/Robin type are enforced at the endpoints of a bounded interval. First, by a careful application of the method of characteristics, we derive a closed-form representation of the solution for an impulsive Dirichlet data at the left endpoint, and valid for either a Neumann or a Robin data at the right endpoint. Then we devise a reconstruction procedure for identifying both the interval length and the Robin parameter. We provide a corresponding stability result and verify numerically its performance moving from a finite element discretization.