Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications

By Oleg Yu. Imanuvilov, Masahiro Yamamoto. 2001

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/89c4941df7c1b725c211537f774ab5c260ee43da

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In Applied Mathematics

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Citations in the corpus

Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients (2002, background): “Among them, let us mention [10], [9], [6], [2], [1], [11], [8] and [4] concerning null controllability, [5], [18], [7], [8] and [4] for approximate controllability, [10] and [8] for exact controllability to the trajectories.”
An Introduction to the Controllability of Partial Differential Equations (2004, background): “Carleman inequalities for parabolic equations: The null controllability of the heat equation with variable coefficients and lower order time-dependent terms has been studied by Fursikov and Imanuvilov (see for instance [16], [26], [27], [28], [34] and [35]).”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, methodology): “This was developed in [98] (see also [63]).”
Null controllability of Grushin-type operators in dimension two (2011, background): “The null and approximate controllability of the heat equation are essentially well understood subjects for both linear and semilinear equations, and for bounded or unbounded domains (see, for instance, [15], [19], [21], [22], [23], [27], [31], [32], [36], [39], [40], [45], [46]).”
On Carleman estimates for hyperbolic equations (2002, unknown): “The ﬁrst result in this direction appeared in the work of Ruiz [27] in which he presents the special case of the wave operator and for functions with compact support (see also [1,33] and [6,7,11,12] for the case of parabolic equations).”
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 OF PARTIAL DIFFERENTIAL EQUATIONS AND ITS SEMI-DISCRETE APPROXIMATIONS (2006, background): “When a ∈ C(1)(Ω) this condition is well-known and may be obtained by means of Carleman Inequalities ([111]).”