References
- Rakesh , Symes WW. Uniqueness for an inverse problem for the wave equation. Comm PDE. 1988;13(1):87–96. doi: 10.1080/03605308808820539
- Eskin G. A new approach to hyperbolic inverse problems. Inverse Probl. 2006;22(3):815–831. doi: 10.1088/0266-5611/22/3/005
- Isakov V. An inverse hyperbolic problem with many boundary measurements. Commun Partial Differ Equ. 1991;16:1183–1195. doi: 10.1080/03605309108820794
- Bellassoued M , Choulli M , Yamamoto M. Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem. J Differ Equ. 2009;247(2):465–494. doi: 10.1016/j.jde.2009.03.024
- Isakov V , Sun Z. Stability estimates for hyperbolic inverse problems with local boundary data. Inverse Probl. 1992;8:193–206. doi: 10.1088/0266-5611/8/2/003
- Sun Z. On continuous dependence for an inverse initial boundary value problem for the wave equation. J Math Anal Appl. 1990;150:188–204. doi: 10.1016/0022-247X(90)90207-V
- Cipolatti R , Lopez IF. Determination of coefficients for a dissipative wave equation via boundary measurements. J Math Anal Appl. 2005;306:317–329. doi: 10.1016/j.jmaa.2004.11.065
- Bellassoued M , Jellali D , Yamamoto M. Lipschitz stability for a hyperbolic inverse problem by finite local boundary data. Appl Anal. 2006;85:1219–1243. doi: 10.1080/00036810600787873
- Ramm AG , Rakesh . Property C and an inverse problem for a hyperbolic equation. J Math Anal Appl. 1991;156:209–219. doi: 10.1016/0022-247X(91)90391-C
- Ben Aïcha I. Stability estimate for hyperbolic inverse problem with time dependent coefficient. Inverse Probl. 2015;31(12).
- Kian Y. Stability in the determination of a time-dependent coefficient for wave equations from partial data. Math Anal Appl. 2016;436:408–428. doi: 10.1016/j.jmaa.2015.12.018
- Kian Y. Unique determination of time-dependent potential for wave equations from partial data. Ann de l'IHP (C), Non Linear Anal. 2017;34(4):973–990.
- Kian Y. Determination of a time-dependent coefficient for wave equations from partial data arxiv: 14.06.5734v2.
- Bellassoued M , Jellali D , Yamamoto M. Stability estimate for the hyperbolic inverse boundary value problem by local Dirichlet-to-Neumann map. J Math Anal Appl. 2008;343(2):1036–1046. doi: 10.1016/j.jmaa.2008.01.098
- Bukhgeim AL , Klibanov MV. Global uniqueness of class of multidimensional inverse problems. Sov Math Dokl. 1981;24:244–247.
- Bellassoued M. Global logarithmic stability in inverse hyperbolic problem by arbitrary boundary observation. Inverse Probl. 2004;20(4):1033–1052. doi: 10.1088/0266-5611/20/4/003
- Immanuvilov OY , Yamamoto M. Determination of a coefficient in an acoustic equation with single measurement. Inverse Probl. 2003;19:157–171. doi: 10.1088/0266-5611/19/1/309
- Imanuvilov OY , Yamamoto M. Global uniqueness and stability in determining coefficients of wave equations. Commun Partial Differ Equ. 2001;26:1409–1425. doi: 10.1081/PDE-100106139
- Kazemi MA , Klibanov MV. Stability estimates for ill-posed Cauchy problems involving hyperbolic equations and inequalities. Appl Anal. 1993;50(1–2):93–102. doi: 10.1080/00036819308840186
- Klibanov MV. Inverse problems and Carleman estimates. Inverse Probl. 1992;8:575–596. doi: 10.1088/0266-5611/8/4/009
- Klibanov MV , Timonov AA. Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
- Bellassoued M , Choulli M. Logarithmic stability in the dynamical inverse problem for the Schrödinger equation by arbitrary boundary observation. J Math Pures Appl. 2009;91(3):233–255. doi: 10.1016/j.matpur.2008.06.002
- Bellassoued M , Yamamoto M. Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation. J Math Pures Appl. 2006;85:193–224. doi: 10.1016/j.matpur.2005.02.004
- Bellassoued M , Yamamoto M. Carleman estimates and applications to inverse problems for hyperbolic systems. 2017. p. 260. (Springer monographs in mathematics. XII).
- Ikawa M. Hyperbolic partial differential equations and wave phenomena. Providence (RI): American Mathematical Soc.; 2000.
- Lasiecka I , Lions J-L , Triggiani R. Non homogeneous boundary value problems for second order hyperbolic operators. J Math Pures Appl. 1986;65:149–192.
- Bellassoued M , Ben Aïcha I. Uniqueness for an hyperbolic inverse problem with time-dependent coefficient. ARIMA Rev Afr Rech Inform Math Appl. 2016;23:65–78.