References
- Ladyzhenskaia OA, Solonnikov VA, Ural’ceva NN. Linear and quasilinear equations of parabolic type. Translations of mathematical monographs. Providence (RI): American Mathematical Society; 1995.
- Di Cristo M, Vessella S. Stable determination of the discontinuous conductivity coefficient of a parabolic equation. SIAM J. Math. Anal. 2010;42:183–217.
- Lions JL, Magenes E. Non-homogeneous boundary value problems and applications. New York (NY): Springer-Verlag; 1972.
- Cantwell WJ, Morton J. The significance of damage and defects and their detection in composite materials: a review. J. Strain Anal. Eng. Des. 1992;27:29–42.
- Elayyan A, Isakov V. On an inverse diffusion problem. SIAM J. Appl. Math. 1997;57:1737–1748.
- Nakamura G, Sasayama S. Inverse boundary value problem for the heat equation with discontinuous coefficients. J. Inverse Ill-Posed Prob. 2013;21:177–352.
- Sylvester J, Uhlmann G. A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 1987;125:153–169.
- Calderón AP. On an inverse boundary value problem. Comput. Appl. Math. 2006;25:133–138, reprint.
- Uhlmann G. Electrical impedance tomography and Calderón’s problem. Inverse Prob. 2009;25:123011.
- Colton D, Päivärinta L. The uniqueness of a solution to an inverse scattering problem for electromagnetic waves. Arch. Ration. Mech. Anal. 1992;119:59–70.
- Chen J, Yang Y. Inverse problem of electro-seismic conversion. Inverse Prob. 2013;29:115006.
- Gaitan P, Isozaki H, Poisson O, Siltanen S, Tamminen J. Inverse problems for time-dependent singular heat conductivities – one-dimensional case. SIAM J. Math. Analysis. 2013;45:1675–1690.
- Noon PJ. The single layer heat potential and Galerkin boundary element methods for the heat equation [Doctor of philosophy]. Baltimore (MD): University of Maryland; 1988.
- Dou FF, Fu CL, Yang FL. Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation. J. Comput. Appl. Math. 2009;230:728–737.
- Fu CL, Dou FF, Feng XL, Qian Z. A simple regularization method for stable analytic continuation. Inverse Prob. 2008;24:065003.
- Murio DA. The mollification method and the numerical solution of ill-posed problems. New York (NY): Wiley; 1993.
- Tanner J. Optimal filter and mollifier for piecewise smooth spectral data. Math. Comput. 2006;75:767–790.