Dynamics of Partial Differential Equations

Volume 14 (2017)

Number 1

Logarithmic stability in determining a boundary coefficient in an IBVP for the wave equation

Pages: 33 – 45

DOI: https://dx.doi.org/10.4310/DPDE.2017.v14.n1.a3

Authors

Kaïs Ammari (UR Analysis and Control of PDE, Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia)

Mourad Choulli (Institut Élie Cartan de Lorraine, Université de Lorraine, Vandoeuvre les Nancy, France)

Abstract

In the article “Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations” [J. Diff. Equat. 259 (7) (2015), 3344-3365] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. The present work deals with an adaptation of that method to obtain a logarithmic stability estimate for the inverse problem of determining a boundary damping coefficient from boundary measurements. As in our preceding work, the different boundary measurements are generated by varying one of the initial conditions.

Keywords

inverse problem, wave equation, boundary damping coefficient, logarithmic stability, boundary measurements

2010 Mathematics Subject Classification

35R30

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Published 31 January 2017