New realization of the pseudoconvexity and its application to an inverse problem

References

• Hörmander , L . 1963 . Linear Partial Differential Operators , Berlin : Springer-Verlag .
   Google Scholar
• Isakov , V . 1990 . Inverse Source Problems , Providence, Rhode Island : American Mathematical Society .
   Google Scholar
• Isakov , V . 1993 . Carleman type estimates in an anisotropic case and applications . J. Diff. Eqns , 105 : 217 – 239 .
   Web of Science ®Google Scholar
• Isakov , V . 1998, 2006 . Inverse Problems for Partial Differential Equations , Berlin : Springer-Verlag .
   Google Scholar
• Isakov , V . 2004 . “ Carleman estimates and their applications ” . In ‘New Analytic and Geometric Methods in Inverse Problems’ , 93 – 127 . Berlin : Springer-Verlag .
   Google Scholar
• Imanuvilov , OYu . 2002 . On Carleman estimates for hyperbolic equations . Asymptotic Anal. , 32 : 185 – 220 .
   Web of Science ®Google Scholar
• Cheng , J , Isakov , V , Yamamoto , M and Zhou , Q . 2003 . Lipschitz stability in the lateral Cauchy problem for elasticity system . J. Math. Kyoto Univ. , 43 : 475 – 501 .
   Google Scholar
• Kazemi , MA and Klibanov , MV . 1993 . Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities . Appl. Anal. , 50 : 93 – 102 .
   Google Scholar
• Lasiecka , I and Triggiani , R . 1997 . Carleman estimates and exact boundary controllability for a system of coupled, nonconservative second-order hyperbolic equations in ‘Partial Differential Equation Methods in Control and Shape Analysis’ , 215 – 243 . New York : Marcel Dekker . (Lecture Notes in Pure and Applied Mathematics, Vol. 188)
   Google Scholar
• Amirov , A and Yamamoto , M . 2008 . A timelike Cauchy problem and an inverse problem for general hyperbolic equations . Appl. Math. Lett. , 21 : 885 – 891 .
   Web of Science ®Google Scholar
• Bellassoued , M . 2004 . Uniqueness and stability in determining the speed of propagation of second-order hyperbolic equation with variable coefficients . Appl. Math. , 83 : 983 – 1014 .
   Google Scholar
• Bukhgeim , AL and Klibanov , MV . 1981 . Global uniqueness of a class of multidimensional inverse problems . Soviet Math. Dokl. , 24 : 244 – 247 .
   Google Scholar
• Imanuvilov , OYu , Isakov , V and Yamamoto , M . 2003 . An inverse problem for the dynamical Lamé system with two sets of boundary data . Comm. Pure Appl. Math. , 56 : 1366 – 1382 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2001 . Global uniqueness and stability in determining coefficients of wave equations . Commun. Partial Differ. Eqns , 26 : 1409 – 1425 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2001 . Global Lipschitz stability in an inverse hyperbolic problem by interior observations . Inverse Probl. , 17 : 717 – 728 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2003 . Determination of a coefficient in an acoustic equation with a single measurement . Inverse Probl. , 19 : 157 – 171 .
   Web of Science ®Google Scholar
• Imanuvilov , OYu and Yamamoto , M . 2005 . Carleman estimates for the non-stationary Lamé system and the application to an inverse problem . ESAIM:COCV , 11 : 1 – 56 .
   Web of Science ®Google Scholar
• Isakov , V . 1989 . Uniqueness of the continuation across a time-like hyperplane and related inverse problems for hyperbolic equations . Commun. Partial Differ. Eqns , 14 : 465 – 478 .
   Web of Science ®Google Scholar
• Isakov , V and Yamamoto , M . 2000 . Carleman estimate with the Neumann boundary condition and its applications to the observability inequality and inverse hyperbolic problems . Contem. Math. , 268 : 191 – 225 .
   Google Scholar
• Khaĭdarov , A . 1987 . Carleman estimates and inverse problems for second order hyperbolic equations . Math. USSR Sbornik , 58 : 267 – 277 .
   Google Scholar
• Klibanov , MV . 1992 . Inverse problems and Carleman estimates . Inverse Probl. , 8 : 575 – 596 .
   Web of Science ®Google Scholar
• Yamamoto , M . 1999 . Uniqueness and stability in multidimensional hyperbolic inverse problems . J. Math. Pures Appl. , 78 : 65 – 98 .
   Web of Science ®Google Scholar
• Romanov , VG . 2006 . Carleman estimates for second-order hyperbolic equations . Siberian Math. J. , 47 : 135 – 151 .
   Web of Science ®Google Scholar
• Lasiecka , I , Triggiani , R and Yao , PF . 1999 . Inverse/observability estimates for second-order hyperbolic equations with variable coefficients . J. Math. Anal. Appl. , 235 : 13 – 57 .
   Web of Science ®Google Scholar
• Yao , PF . 1999 . On the observability inequalities for exact controllability of wave equations with variable coefficients . SIAM J. Control Optim. , 37 : 1568 – 1599 .
   Web of Science ®Google Scholar
• Romanov , VG . 1987 . Inverse Problems of Mathematical Physics , Utrecht : VNU Science Press .
   Google Scholar
• Lasiecka , I , Triggiani , R and Zhang , X . 2000 . Nonconservative wave equations with unobserved Neumann B.C.: Global uniqueness and observability in one shot . Contem. Math. , 268 : 227 – 325 .
   Google Scholar