[1] R. A. Adams, Sobolev Spaces, 2nd Edition, Academic Press, New York, 1975.
[2] P. Albano, Carleman estimates for the Euler-Bernoulli plate operator, Elec. J. of Diff. Equ. 53, 2000, 1-13.
[3] R. Aris, Vectors, tensors, and the basic equations of fluid mechanics, Englewood Cliffs, Prentice-Hall, NJ, 1962.
[4] L. Baudouin, J. -P. Puel, Uniqueness and stability in an inverse problem for the Schr¨odinger equation, Inverse Problems 18, 2002, 1537-1554.
[5] M. Bellassoued, M. Choulli, Logarithmic stability in the dynamical inverse problem for the Schr¨odinger equation by arbitrary boundary observation, J. Math. Pures Appl. 91 no. 3, 2009, 233-255.
[6] M. Bellassoued, M. Choulli, Stability estimate for an inverse problem for the magnetic Schr¨odinger equation from the Dirichlet-to-Neumann map, Journal of Functional Analysis 91 no. 258, 2010, 161-195.
[7] M. Bellassoued, M. Cristofol, E. Soccorsi, Inverse boundary value problem for the dynamical heterogeneous Maxwell system, Inverse Problems 28 no. 9, 2012, 095009, 18 pp.
[8] M. Bellassoued, O. Y. Imanuvilov, M. Yamamoto, Carleman estimate for the Navier-Stokes equations and an application to a lateral Cauchy problem, Inverse Problems 32 no. 2, 2016.
[9] M. Bellassoued, Y. Kian, E. Soccorsi, An inverse stability result for non compactly supported potentials by one arbitrary lateral Neumann observation, Journal of Differential Equations 260 no. 10, 2016, 7535-7562.
[10] M. Bellassoued, M. Yamamoto, Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, Springer-Japan, Tokyo, 2017.
[11] I. Ben Aicha, Y. Mejri, Simultaneous determination of the magnetic field and the electric potential in the Schr¨odinger equation by a finite number of observations, Journal of Inverse and Ill-Posed Problems 26 no. 2, 2018, 201-209.
[12] H. Ben Joud, A stability estimate for an inverse problem for the Schr¨odinger equation in a magnetic field from partial boundary measurements, Inverse Problems 25 no. 4, 2009, 45012-45034.
[13] D. A. Benson et al., Application of a fractional advection-dispersion equation, Water Resource Research 36, 2000, 1403-1412.
[14] A. L. Bukhgeim, M. V. Klibanov, Global Uniqueness of a class of multidimensional inverse problems, Sov. Math. Dokl. 24, 1981, 244-247.
[15] T. Carleman, Sur un probleme d’unicite pour les systemes d’equations aux derivees partielles a deux variables independentes, Ark. Mat. Astr. Fys. 2 B, 1939, 1-9.
[16] D. Chae, O. Y. Imanuvilov, S. M. Kim, Exact Controllability for Semilinear Parabolic Equations with Neumann Boundary Conditions, Journal of Dynamical and Control Systems 2 no. 4, 1996, 449-483.
[17] J. Cheng, J. Nakagawa, M. Yamamoto, T. Yamazaki, Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation, Inverse problems 25 no. 11, 2009, 115002.
[18] M. Choulli, O. Y. Imanuvilov, J. -P. Puel, M. Yamamoto, Inverse source problem for linearized Navier-Stokes equations with data in arbitrary sub-domain, Applicable Analysis 92, 2013, 2127-2143.
[19] M. Choulli, Y. Kian, E. Soccorsi, Stable determination of time-dependent scalar potential from boundary measurements in a periodic quantum waveguide, SIAM Journal on Mathematical Analysis 47 no. 6, 2015, 4536-4558.
[20] M. Cristofol, S. Li, E. Soccorsi, Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary, Mathematical Control and Related Fields 6 no. 3, 2016, 407-427.
[21] M. Cristofol, E. Soccorsi, Stability estimate in an inverse problem for non-autonomous Schr¨odinger equations, Applicable Analysis 90 no. 10, 2011, 1499-1520.
[22] Y. V. Egorov, Linear Differential Equations of Principal Type, Consultants Bureau, New York, 1986.
[23] G. Eskin, Inverse boundary value problems and the Aharonov-Bohm effect, Inverse Problems 19, 2003, 49-62.
[24] G. Eskin, Inverse problems for the Schr¨odinger operators with electromagnetic potentials in domains with obstacles, Inverse Problems 19, 2003, 985-996.
[25] G. Eskin, Inverse problems for the Schr¨odinger equations with time-dependent electromagnetic potentials and the Aharonov-Bohm effect, J. Math. Phys. 49 no. 2, 2008, 022105, 18 pp.
[26] J. Fan, J. Li, A logarithmic regularity criterion for the 3D generalized MHD system, Math. Meth. Appl. Sci., doi: 10.1002/mma.3480, 2015.
[27] D. Dos Santos Ferreira, C. E. Kenig, J. Sj¨ostrand, G. Uhlmann, Determining a magnetic Schr¨odinger operator from partial Cauchy data, Comm. Math. Phys. 2, 2007, 467–488.
[28] A. V. Fursikov, O. Y. Imanuvilov, Controllability of Evolution Equations, Seoul National University, Korea, 1996.
[29] P. Gaitan, H. Ouzzane, Inverse problem for a free transport equation using Carleman estimates, Applicable Analysis, http://dx.doi.org/10.1080/00036811.2013.816686, 2013.
[30] R. Haggerty et al., Powerlaw residence time distribution in the hyporheic zone of a 2ndorder mountain stream, Geophysical Research Letters 29 Issue 13, 2002, 18-1-18-4.
[31] Y. Hatano, N. Hatano, Dispersive transport of ions in column experiments: an explanation of long-tailed profiles, Water Resources Research 34 no. 5, 1998, 1027-1033.
[32] T. Havˆarneanu, C. Popa, S. S. Sritharan, Exact internal controllability for the magnetohydrodynamic equations in multi-connected domains, Adv. Differential Equations 11 no. 8, 2006, 893-929.
[33] T. Havˆarneanu, C. Popa, S. S. Sritharan, Exact internal controllability for the twodimensional magnetohydrodynamic equations, SIAM J. CONTROL OPTIM. 46 no. 5, 2007, 1802-1830.
[34] L. H¨ormander, The Analysis of Linear Partial Differential Operators I − IV , Springer, Berlin, 1985.
[35] O.Y. Imanuvilov, Controllability of parabolic equations, Sbornik Math. 186, 1995, 879-900.
[36] O. Y. Imanuvilov, J. -P. Puel, Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems, IMRN 16, 2003, 883-913.
[37] O. Y. Imanuvilov, J. -P. Puel, M. Yamamoto, Carleman estimates for parabolic equations with nonhomogeneous boundary conditions, Chin. Ann. Math. Ser. B 30, 2009, 333-378.
[38] O.Y. Imanuvilov, M. Yamamoto, Global Lipschitz stability in an inverse hyperbolic problem by interior observations, Inverse Problems 17 no. 4, 2001, 717-728.
[39] V. Isakov, Inverse Source Problems, American Mathematical Society, Providence, RI, 1990.
[40] V. Isakov, Inverse Problems for Partial Differential Equations, Springer, Berlin, 1998.
[41] D. Jiang, Z. Li, Y. Liu, M. Yamamoto, Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations, Inverse Problems 33, 2017, 055013.
[42] Y. Kian, Q. S. Phan, E. Soccorsi, Carleman estimate for infinite cylindrical quantum domains and application to inverse problems, Inverse Problems 30 no. 5, 2014, 055016, 16 pp.
[43] Y. Kian, Q.S. Phan, E. Soccorsi, H¨older stable determination of a quantum scalar potential in unbounded cylindrical domains, Journal of Mathematical Analysis and Applications 426 no. 1, 2015, 194-210.
[44] Y. Kian, E. Soccorsi, H¨older stably determining the time-dependent electromagnetic potential of the Schr¨odinger equation, To appear at SIAM J. on Math. Anal., arXiv:1705.01322.
[45] M.V. Klibanov, Inverse problems in the ‘large’ and Carleman bounds, Differential Equations 20 no. 6, 1984, 755-760.
[46] M. V. Klibanov, A class of inverse problems for nonlinear parabolic equations, Siberian Mathematical Journal 27 Issue 5, 1987, 698-707.
[47] M. V. Klibanov, Inverse problems and Carleman estimates, Inverse Problems 8, 1992, 575- 596.
[48] M. V. Klibanov, A. A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications, VSP, Utrecht, 2004.
[49] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, 2006.
[50] I.O. Kulik, R. Ellialtiogammalu, Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics, NATO Science Series, Series C, Mathematical and Physical Sciences, Vol. 559, Springer-Verlag, 2000.
[51] O.A. Ladyzhenskaya, V.A. Solonnikov, Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids, Journal of Soviet Mathematics 9, 1978, 697-749.
[52] M. Levy, B. Berkowitz, Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, Journal of contaminant hydrology 64 no. 3, 2003, 203-226.
[53] T. Li, T. Qin, Physics and Partial Differential Equations, Higher Education Press, Beijing, Vol. 1, 2013.
[54] Z. Li, Mathematical analysis for diffusion equations with generalized fractional time derivatives, PhD Thesis, Graduate School of Mathematical Sciences, The University of Tokyo, 2016.
[55] Z. Li, O. Y. Imanuvilov, M. Yamamoto, Uniqueness in inverse boundary value problems for fractional diffusion equations, Inverse Problems 32 no. 1, 2016, 015004.
[56] Z. Li, M. Yamamoto, Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation, Applicable Analysis 94 no. 3, 2015, 570- 579.
[57] J. -L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Translated from the French by P. Kenneth, Vol. 2, Springer-Verlag, Berlin, 1972.
[58] H. Lin, L. Du, Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions, IOP Publishing Ltd & London Mathematical Society, Nonlinearity, Vol.26, no. 1, 2013, 219-239.
[59] F. Mainardi, A. Mura, G. Pagnini, et al., Time-fractional diffusion of distributed order, Journal of Vibration and Control 14(9-10), 2008, 1267-1290.
[60] A. Mercado, A. Osses, L. Rosier, Inverse problems for the Schr¨odinger equation via Carleman inequalities with degenerate weights, Inverse Problems 24 no. 1, 2008, 015017.
[61] G. Nakamura, Z. Sun, G. Uhlmann, Global identifiability for an inverse problem, Math.Ann. 303, 1995, 377-388.
[62] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
[63] K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusionwave equations and applications to some inverse problems, Journal of Mathematical Analysis and Applications 382 no. 1, 2011, 426-447.
[64] M. Salo, Inverse problem for nonsmooth first order perturbation of the Laplacian, Ann. Acad. Sci. Fenn. Math. Dissertations 139, 2004.
[65] R. Schumer, D. A. Benson, Fractal mobile/immobile solute transport, Water Resource Research 39 no. 10, 2003.
[66] Z. Sun, An inverse boundary problem boundary value problem for the Schr¨odinger operator with vector potentials, Trans. Am. Math. Soc. 338, 1992, 953-969.
[67] D. Tataru, Carleman estimates and unique continuation for solutions to boundary value problems, J. Math. Pures Appl. 75, 1996, 367-408.
[68] D. Tataru, Carleman Estimates, Unique Continuation and Controllability for anisotropic PDEs, Cont. Math. 209, 1997, 267-279.
[69] M. Taylor, Pseudodifferential Operators, Princeton University Press, Princeton, NJ, 1981.
[70] C.F. Tolmasky, Exponentially growing solutions for nonsmooth first-order perturbations of the Laplacian, SIAM J. Math. Anal. 29 no. 1, 1998, 116-133.
[71] L. Tzou, Stability estimates for coefficients of magnetic Schr¨odinger equation from full and partial boundary measurements, Comm. Part. Diff. Equ. 33, 2008, 1911-1952.
[72] X. Xu, J. Cheng, M. Yamamoto, Carleman estimate for a fractional diffusion equation with half order and application, Applicable Analysis 90 no. 9, 2011, 1355-1371.
[73] M. Yamamoto, Uniqueness and stability in multidimensional hyperbolic inverse problems, J. Math. Pures Appl. 78, 1999, 65-98.
[74] M. Yamamoto, Carleman estimates for parabolic equations and applications, Inverse Problems 25 no. 12, 2009, 123013.
[75] G. Yuan, M. Yamamoto, Carleman estimates for the Schr¨odinger equation and applications to an inverse problem and an observability inequality, Chin. Ann. Math. Ser. B 31, 2010, 555-578.
[76] Z. Zhang, An undetermined coefficient problem for a fractional diffusion equation, Inverse Problems 32 no. 1, 2016, 015011.