NULL CONTROLLABILITY OF THE HEAT EQUATION WITH BOUNDARY FOURIER CONDITIONS: THE LINEAR CASE ∗

By Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel. 2006

121 citations recorded by the source corpus.

In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ∂y ∂n + βy = 0. We consider distributed controls with support in a small set and nonregular coefficients β = β(x, t). For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.

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

View Paper: https://www.semanticscholar.org/paper/df9db2b7f81ae73eb85b157f837650348a8eb329

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Citations in the corpus

Controllability of systems of Stokes equations with one control force: existence of insensitizing controls (2007, unknown): “Then, one can follow the steps of the proof in [5] (see Theorem 1 in that reference) and adapt the arguments just taking into account that ∂tα := αt ≤ KTξ and ∂ttα := αtt ≤ CT (2)ξ, (21) with K > 0 independent of s, λ and T .”
Optimal Shape and Location of Sensors for Parabolic Equations with Random Initial Data (2014, background): “It is well known that, if Ω is C, then this observability inequality holds true (see [17, 20, 39, 61]).”
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].”
Null controllability of the N-dimensional Stokes system with N−1 scalar controls (2009, background): “Then, one can follow the steps of the proof in [3] (see Theorem 1 in that reference) and adapt the arguments just taking into account that ∂tα := αt CT ξ10/9 and ∂ttα := αtt CT 2ξ11/9, (15) with C > 0 independent of s, λ and T .”