Carleman Inequalities for Parabolic Equations in Sobolev Spaces of Negative Order and Exact Controllability for Semilinear Parabolic Equations

By Oleg Yu. Imanuvilov, Masahiro Yamamoto. 2003

174 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f4695024e4dcadd45598d05fdc545ef65ce9eb95

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Citations in the corpus

Lipschitz stability in the determination of the principal part of a parabolic equation (2009, methodology): “As for Carleman estimates for parabolic equations with singular weight function φ(t, x), we can refer to Fursikov and Imanuvilov [15], Imanuvilov [19], Imanuvilov and Yamamoto [22,24], and such Carleman estimates hold for a function v not satisfying v(τ1, ·) = v(τ2, ·) = 0.”
A Kalman rank condition for the localized distributed controllability of a class of linear parabolic systems (2009, background): “The proof of this result can be found in [15] although the authors do not specify the way the constant s0 depends on T .”
Global Carleman estimate for stochastic parabolic equations, and its application (2014, methodology): “Further, following the method used in [9], one has the following more general Carleman estimate for equation (4.”
Insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient (2004, background): “The first insensitivity result we present in this paper is the following one: Theorem 1.1 Assume that ω ∩ O 6= ∅ and y0 = 0.”
Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems (2002, methodology): “In order to ﬁnd stability inequalities for inverse problems, a global Carleman inequality is proved in [7] for solutions of parabolic equations with right-hand sides in H 1 but with homogeneous Dirichlet boundary value.”
Control and Stabilization Properties for a Singular Heat Equation with an Inverse-Square Potential (2008, methodology): “Later, in [14], this result has been extended to the case V ∈ L∞((0, T );L(Ω)).”
Carleman estimates for degenerate parabolic equations with first order terms and applications (2010, background): “:3) s 0 and let us introduce the null controllability problem: Following [10] it is possible to prove that inequality (10) implies the existence of such a control and that inequality (11) is satisﬁed .”
Carleman estimates for parabolic equations with nonhomogeneous boundary conditions (2009, background): “Global Carleman estimates for parabolic equations with homogeneous boundary conditions have been obtained by several authors in the recent years (see for example [9] for L 2 (0 ,T ; L 2 (Ω)) right-hand sides and [ 13 ] for L 2 (0 ,T ; H −1 (Ω)) right-hand sides).”