Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem

By Assia Benabdallah, Y. Dermenjian, Jérôme Le Rousseau. 2007

83 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9155f4a56503f8a9f216633ff31852d325a9cce2

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Citations in the corpus

Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces (2011, background): “In one dimension in space, the monotonicity condition was relaxed in [ 3 ].”
A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems (2009, background): “2) with non smooth coefficients rij (see [6], [5] and [19] for exact assumptions).”
DEGENERATE PARABOLIC OPERATORS OF KOLMOGOROV TYPE WITH A GEOMETRIC CONTROL CONDITION (2015, background): “1 Null controllability of the heat equation The null and approximate controllabilities of the heat equation are essentially well understood subjects for both linear and semilinear equations, for bounded or unbounded domains [3, 27, 30, 32, 33, 34, 37, 44, 46, 48, 51, 52, 62, 63] and also with discon”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, background): “The results on semi-linear equations have been extended to the case of non smooth coefficients [7,14,34,36].”
Carleman estimates for parabolic equations and applications (2009, background): “As for the inverse problems for parabolic equations with discontinuous coefficients of the principal term, see [11, 15, 16, 126].”
Null controllability of Grushin-type operators in dimension two (2011, unknown): “[16], [4], [5], [42]) or singular ([43] and [18]) coe cients.”
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 (2010, methodology): “Recently, in the one-dimensional case, the controllability result for parabolic equations was proven for general piecewise C 1 coefficients in [ 2 ], and for coeffi-”
Control and Stabilization Properties for a Singular Heat Equation with an Inverse-Square Potential (2008, methodology): “7), we will use a particular Carleman estimate, which is by now a classical technique in control theory, see for instance [2, 9, 10, 11, 12, 13, 14].”