A direct Lebeau-Robbiano strategy for the observability of heat-like semigroups

By Luc Miller. 2010

127 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/553e368562251bbebae00113ab1a5f3b1c18e1db

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In Computational Theory and Mathematics

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Citations in the corpus

Sharp Observability Estimates for Heat Equations (2011, methodology): “Observe also that, as pointed out in [43] and recently further developed in [27], these estimates and their optimality are intimately related with the spectral estimates by Lebeau and Robbiano [22] on the observability of packets of eigenfunctions.”
On the null-controllability of diffusion equations (2011, methodology): “Appealing to a simplification of the methodology proposed in [4] and developed in [7,8,10] we give below sufficient conditions for the solvability of this moment problem and provide estimates for the solution Θ.”
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations (2012, background): “Some recent results are available with some lower bonds and uperbounds [47,57].”
Null-controllability of hypoelliptic quadratic differential equations (2016, unknown): “It is inspired from the works [47, 48] with a modification suggested to us by the author.”
Observability Inequalities and Measurable Sets (2012, methodology): “3) (where ∂Ω is smooth) were essentially first established, via the Lebeau-Robbiano spectral inequalities in [28] (See also [29, 34, 16]).”
Spectral estimates for finite combinations of Hermite functions and null-controllability of hypoelliptic quadratic equations (2018, result): “The proof of the above result is inspired by [37, 38].”
Quantitative approximation properties for the fractional heat equation (2017, background): “for instance [11, 13, 27, 25, 31, 32, 33, 41] and in particular [2, 30, 29] for the setting of non-local equations and the references therein), in the present article, motivated by applications to inverse problems, we seek to approximate a given function at each time slice by choosing suitable exter”
Sharp estimates and homogenization of the control cost of the heat equation on large domains (2018, unknown): “Since then the bounds on the control cost have received a lot of attention [1, 3, 7, 11–13, 22, 23, 27, 28, 30, 32–35, 38, 39, 43, 44].”