Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T19:21:29.718Z Has data issue: false hasContentIssue false
  • English
  • Français

Null controllabilityof nonlinear convective heat equations

Published online by Cambridge University Press:  15 August 2002

Sebastian Aniţa and
Viorel Barbu
Sebastian Aniţa
Affiliation:
Faculty of Mathematics, University “Al.I. Cuza", 6600 Iaşi, Romania.
Viorel Barbu
Affiliation:
Faculty of Mathematics, University “Al.I. Cuza", 6600 Iaşi, Romania.
Get access

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 Lk .

Keywords

Null controllabilityCarleman estimatesinterpolation inequalityKakutani fixed point theorem.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000, pp. 157 - 173
Copyright
© EDP Sciences, SMAI, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).
V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic Press, Boston (1993).
V. Barbu, Exact controllability of the superlinear heat equation. Appl. Math. Optim., to appear.
V. Barbu, T. Precupanu, Convexity and Optimization in Banach Spaces. D. Reidel Publ. Company, Dordrecht (1986).
Brézis, H. and Friedman, A., Nonlinear parabolic equations involving measures as initial conditions. J. Math. Pures Appl. 62 (1983) 73-97.
K. Deimling, Nonlinear Functional Analysis. Springer-Verlag, Berlin (1985).
C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation, Proceedings Royal Soc. Edinburgh 125 A (1995) 31-61.
Fernández-Cara, E., Null controllability of the semilinear heat equation. ESAIM Control. Optim. Calc. Var. 2 (1997) 87-107.
E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: The linear case. Adv. Diff. Equations, to appear.
E. Fernández-Cara and E. Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations. Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear.
A.V. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. RIM Seoul National University, Korea, Lecture Notes Ser. 34 (1996).
O.Yu. Imanuvilov and M. Yamamoto, On Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, preprint #98 - 46. University of Tokyo, Grade School of Mathematics, Komobo, Tokyo, Japan (1998).
O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uraltzeva, Linear and Quasilinear Equations of Paraboic Type. Nauka, Moskow (1967).
Lebeau, G. and Robbiano, L., Contrôle exact de l'équation de la chaleur. Comm. Partial Differential Equations 30 (1995) 335-357. CrossRef
J.L. Lions, Contrôle des systèmes distribués singuliers, MMI 13. Gauthier-Villars (1983).
J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968).
E. Zuazua, Approximate controllability of the semilinear heat equation: boundary control, in Computational Sciences for the 21st Century, M.O. Bristeau et al., Eds. John Wiley & Sons (1997) 738-747.
E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control Cybernet., to appear.