Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients

By Anna Doubova, Axel Osses, Jean-Pierre Puel. 2002

79 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/614f5796c4f5d23555d7c757091631c989e5d553

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Carleman estimates for parabolic equations and applications (2009, background): “Under some geometrical constraints on the interface of the break of the continuity of a, Carleman estimates are proved: [13, 15, 16, 42, 116, 117, 126].”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, unknown): “For these questions we refer to [4,15,18,22].”
Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces (2011, methodology): “In control theory, global Carleman estimates for parabolic operators yield the null controllability of classes of semi-linear parabolic equations [1, 8, 9]. This last application was the motivation for the proof of a global Carleman estimate in [ 7 ] in the case of a non smooth diffusion coefficient”
Null controllability of Grushin-type operators in dimension two (2011, unknown): “[16], [4], [5], [42]) or singular ([43] and [18]) coe cients.”
Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem (2007, methodology): “heat equation with a discontinuous coefficient was proven in [1] by means of a Carleman observability estimate.”
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): “... X0 > 0. We provide such a local Carleman estimate for the operator A in a small neighborhood V of a point (y0, y) of (0, X0) × S with an “observation” on one side of S, independently of the sign of the jump of c at (y0, y). We hence treat all possible cases including the case that can be treated”
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”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, methodology): “The results in this section do not require the monotonicity conditions in [46].”