References
- Lions , JL and Magenes , E . 1968 . Problèmes aux limites non homogènes et applications , Vol. 1 , Paris : Dunod .
- Pazy , A . 1984 . Semigroups of Linear Operators and Applications to Partial Differential Equations , Vol. 44 , New York : A.M.S, Springer-Verlag .
- Doubova , A , Osses , A and Puel , J-P . 2002 . Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients . ESAIM COCV , 8 : 621 – 661 .
- Klibanov , MV and Timonov , A . 2004 . Carleman Estimates For Coefficient Inverse Problems And Numerical Applications , Utrecht, , Boston : Brill Academic Publishers, VSP .
- Poisson , O . 2008 . Uniqueness and Hölder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation . Inverse Problems , 24 : 32 025012
- Imanuvilov , OY and Yamamoto , M . 2003 . Carleman inequalities for parabolic equations in sobolev spaces of negative order and exact controllability for semilinear parabolic equations . RIMS, Kyoto Univ. , 39 ( 2 ) : 227 – 274 .
- Bukhgeim , AL and Klibanov , MV . 1981 . Global uniqueness of a class of multidimensional inverse problems . Soviet Math. Dokl. , 24 : 244 – 247 .
- Fursikov , A and Yu Imanuvilov , O . 1996 . Controllability of evolution equations . Seoul National University, Korea. Lecture Notes , 34 : 1 – 63 .
- Barbu , V . 2000 . Exact Controllability of the superlinear heat equation . Appl. Math. Optim , 42 : 73 – 89 .
- Doubova , A . 2002 . On the controllability of parabolic systems with a nonlinear term involving the state and the gradient . SIAM J. Control Optim. , 41 : 798 – 819 .
- Fernández-Cara , E and Zuazua , E . 2000 . Null and approximate controllability for weakly blowing up semilinear heat equations . Ann. Inst. H. Poincaré, Analyse non linéaire. , 17 : 583 – 616 .
- Benabdallah , A , Dermenjian , Y and Le Rousseau , J . 2007 . On the controllability of linear parabolic equations with an arbitrary control location for a stratified media . C. R. Acad. Sci, Paris, Ser. I , 344 : 357 – 362 .
- Le Rousseau , J . 2007 . Carleman estimate and controllability results for the one–dimensional heat equation with bv coefficients . J. Diff. Equat. , 233 : 417 – 447 .
- Le Rousseau , J and Robbiano , L . 2007 . “ Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations ” . In CNRS HAL (on web): hal-00193885, version 1 2007. Available online at: http://hal.archives-cuverts.fr/hal-00193885/fr/ (accessed 27 May 2008)
- Hormander , L . 1983 . The Analysis of Linear Partial Differential Equations , Berlin : Springer-Verlag .