Null controllability of nonlinear convective heat equations

Free access article

Issue		ESAIM: COCV Volume 5, 2000


Page(s)		157 - 173
DOI		10.1051/cocv:2000105

DOI: 10.1051/cocv:2000105

ESAIM: COCV, February 2000, Vol. 5, p. 157-173

Null controllability of nonlinear convective heat equations

Sebastian Anita
Faculty of Mathematics, University "Al.I. Cuza", 6600 Iasi, Romania.

Viorel Barbu
Faculty of Mathematics, University "Al.I. Cuza", 6600 Iasi, Romania.

Received January 30, 1999. Revised December 24, 1999.

Abstract: 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 L^k.

Keywords and phrases: Null controllability, Carleman estimates, interpolation inequality, Kakutani fixed point theorem.

AMS Subject Classification: 93B05, 35K05, 46B70, 46E35

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