Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Ammari, Kais¹  Choulli, Mourad² 

[1] Univ Monastir, UR Anal & Control PDE, Fac Sci Monastir, Dept Math,UR 13ES64, Monastir 5019, Tunisia

[2] Univ Lorraine, Inst Elie Cartan Lorraine, CNRS, UMR 7502, F-57045 Metz 01, France

关键词: Damping coefficient;    Potential;    Dissipative wave equation;    Boundary measurements;    Boundary observability;    Initial-to-boundary operator;   

DOI  :  10.1016/j.jde.2015.04.023

来源: Elsevier

【 摘 要 】

We are concerned with the inverse problem of determining both the potential and the damping coefficient in a dissipative wave equation from boundary measurements. We establish stability estimates of logarithmic type when the measurements are given by the operator who maps the initial condition to Neumann boundary trace of the solution of the corresponding initial-boundary value problem. We build a method combining an observability inequality together with a spectral decomposition. We also apply this method to a clamped Euler-Bernoulli beam equation. Finally, we indicate how the present approach can be adapted to a heat equation. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free