Advanced Search
Article Contents
Article Contents

Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary

Abstract Related Papers Cited by
  • We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove Hölder stability with the aid of a Carleman estimate specifically designed for hyperbolic waveguides.
    Mathematics Subject Classification: Primary: 35R30, 35L30.


    \begin{equation} \\ \end{equation}
  • [1]

    M. Bellassoued, Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation, Inverse Problems, 20 (2004), 1033-1052.doi: 10.1088/0266-5611/20/4/003.


    M. Bellassoued, Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients, Applicable Analysis, 83 (2004), 983-1014.doi: 10.1080/0003681042000221678.


    M. Bellassoued, M. Cristofol and E. Soccorsi, Inverse boundary value problem for the dynamical heterogeneous Maxwell's system, Inverse Problems, 28 (2012), 095009, 18pp.doi: 10.1088/0266-5611/28/9/095009.


    M. Bellassoued, M. Choulli and M. Yamamoto, Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem, J. Diff. Equat., 247 (2009), 465-494.doi: 10.1016/j.jde.2009.03.024.


    M. Bellassoued, D. Jellali and M. Yamamoto, Lipschitz stability in in an inverse problem for a hyperbolic equation with a finite set of boundary data, Applicable Analysis, 87 (2008), 1105-1119.doi: 10.1080/00036810802369231.


    M. Bellassoued and M. Yamamoto, Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation, J. Math. Pures Appl., 85 (2006), 193-224.doi: 10.1016/j.matpur.2005.02.004.


    M. Bellassoued and M. Yamamoto, Determination of a coefficient in the wave equation with a single measurement, Applicable Analysis, 87 (2008), 901-920.doi: 10.1080/00036810802369249.


    A. L. Bukhgeim and M. V. Klibanov, Global uniqueness of class of multidimentional inverse problems, Soviet Math. Dokl., 24 (1981), 244-247.


    L. Cardoulis, M. Cristofol and P. Gaitan, Inverse problem for the Schrödinger operator in an unbounded strip, C. R. Math. Acad. Sci. Paris, 346 (2008), 635-640.doi: 10.1016/j.crma.2008.04.004.


    L. C. Evans, Partial Differential Equations, Amer. Math. Soc., Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.doi: 10.1090/gsm/019.


    O. Imanuvilov and M. Yamamoto, Global Lipschitz stability in an inverse hyperbolic problem by interior observations, Inverse Problems, 17 (2001), 717-728.doi: 10.1088/0266-5611/17/4/310.


    O. Imanuvilov and M. Yamamoto, Determination of a coefficient in an acoustic equation with single measurement, Inverse Problems, 19 (2003), 157-171.doi: 10.1088/0266-5611/19/1/309.


    V. Isakov and Z. Sun, Stability estimates for hyperbolic inverse problems with local boundary data, Inverse Problems, 8 (1992), 193-206.doi: 10.1088/0266-5611/8/2/003.


    V. Isakov, Inverse Problems for Partial Differential Equations, Springer-Verlag, Berlin, 2006.


    Y. Kian, Q. S. Phan and E. Soccorsi, Carleman estimate for infinite cylindrical quantum domains and application to inverse problems, Inverse Problems, 30 (2014), 055016, 16pp.doi: 10.1088/0266-5611/30/5/055016.


    Y. Kian, Q. S. Phan and E. Soccorsi, Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains, Journal of Mathematical Analysis and Applications, 426 (2015), 194-210.doi: 10.1016/j.jmaa.2015.01.028.


    M. V. Klibanov and J. Malinsky, Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data, Inverse Problems, 7 (1991), 577-596.doi: 10.1088/0266-5611/7/4/007.


    M. V. Klibanov and M. Yamamoto, Lipschitz stability of an inverse problem for an accoustic equation, Applicable Analysis, 85 (2006), 515-538.doi: 10.1080/00036810500474788.


    J.-L. Lions and E. Magenes, Problèmes aux Limites non Homogènes et Applications, vol. 1, Dunod, 1968.


    P. Stefanov and G. Uhlmann, Stability estimates for the hyperbolic Dirichlet to Neumann map in anisotropic media, J. Funct. Anal., 154 (1998), 330-358.doi: 10.1006/jfan.1997.3188.


    M. Yamamoto, Uniqueness and stability in multidimensional hyperbolic inverse problems, J. Math. Pures Appl., 78 (1999), 65-98.doi: 10.1016/S0021-7824(99)80010-5.

  • 加载中

Article Metrics

HTML views() PDF downloads(125) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint