A uniqueness result for a nonlinear hyperbolic equation

References

• Adams , RA . 1978 . Sobolev Spaces , New York : Academic Press .
   Google Scholar
• Bainov , D and Simeonov , P . 1992 . Integral inequalities and applications , Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Besov , O , Il'in , VP and Nikol'ski , SM . 1979 . Integral Transforms of Functions and Embedding Theorems , Vol. II , Washington , DC : V.H. Winston and Sons .
   Google Scholar
• Cannon , JR . 1967 . Determination of the unknown coefficient k(u) in the equation ∇k(u) ∇ u = 0 from overspecified boundary data . Journal of Mathematical Analysis and Applications , 18 : 112 – 114 .
   Web of Science ®Google Scholar
• Cannon , JR and DuChateau , P . 1980 . An inverse problem for a nonlinear diffusion equation . SIAM Journal on Applied Mathematics , 39 : 272 – 289 .
   Web of Science ®Google Scholar
• Damjanovic , D and Demartin , M . 1996 . The Rayleigh law in piezoelectric ceramics . Journal of Physics D-Applied Physics , 29 : 2057 – 2060 .
   Web of Science ®Google Scholar
• DuChateau , P and Rundell , W . 1985 . Unicity in an inverse problem for an unknown reaction term in a reaction–diffusion equation . Journal of Differential Equations , 59 : 155 – 164 .
   Web of Science ®Google Scholar
• Egger , H , Engl , HW and Klibanov , MV . 2005 . Global uniqueness and Hölder stability for recovering a nonlinear source term in a parabolic equation . Inverse Problems , 21 : 271 – 290 .
   Web of Science ®Google Scholar
• Engl , HW , Hanke , M and Neubauer , A . 1996 . Regularization of Inverse Problems , Dortdrecht : Kluwer .
   Google Scholar
• Isakov , V . 1993 . On uniqueness in inverse problems for semilinear parabolic equations . Archive for Rational Mechanics and Analysis , 124 : 1 – 12 .
   Web of Science ®Google Scholar
• Isakov , V and Nachman , AI . 1995 . Global uniqueness for a two–dimensional semilinear elliptic inverse problem . Transactions of Americans Mathematical Society , 347 : 3375 – 3390 .
   Web of Science ®Google Scholar
• Kaltenbacher , B . 2006 . “ Identification of nonlinear parameters in hyperbolic PDEs, with application to piezoelectricity ” . In Optimal Control of Coupled Systems of PDEs , Edited by: Kunisch , K. , Leugering , G. , Sprekels , J. and Tröltzsch , F. Oberwolfach, April 2005 : Springer .
   Google Scholar
• Kang , H and Nakamura , G . 2002 . Identification of nonlinearity in a conductivity equation via the Dirichlet-to-Neumann map . Inverse Problems , 18 : 1079 – 1088 .
   Web of Science ®Google Scholar
• Lorenzi , A and Lunardi , A . 1990 . An identification problem in the theory of heat conduction . Differential and Integral Equations , 3 : 237 – 252 .
   Google Scholar
• Maugeri , A , Palagachev , DK and Softova , LG . 2000 . Elliptic and Parabolic Equations with Discontinuous Coefficients , Berlin : Wiley-VCH .
   Google Scholar
• Pilant , M and Rundell , W . 1987 . An inverse problem for a nonlinear elliptic differential equation . SIAM Journal on Mathematical Analysis , 18 : 1801 – 1809 .
   Web of Science ®Google Scholar