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Zbl 1106.93009
Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre
Null controllability of the heat equation with boundary Fourier conditions: the linear case.
(English)
[J] ESAIM, Control Optim. Calc. Var. 12, 442-465 (2006). ISSN 1292-8119; ISSN 1262-3377/e

Summary: In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form ${\partial y\over\partial n} + \beta\,y = 0$. We consider distributed controls with support in a small set and nonregular coefficients $\beta=\beta(x,t)$. 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.
MSC 2000:
*93B05 Controllability
35K20 Second order parabolic equations, boundary value problems
49J20 Optimal control problems with PDE (existence)

Keywords: controllability; heat equation; Fourier conditions

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