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kakutani fixed point theorem.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Null controllabilityof nonlinear convective heat equations
Sebastian Aniţa, Viorel Barbu
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 5 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 157-173

Print publication:

2000
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The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in Lk .