Null controllability of the semilinear heat equation

E. Fernandez-Cara

doi:10.1051/cocv:1997104

Abstract

This paper is concerned with the null controllability of systems governed by semilinear parabolic equations. The control is exerted either on a small subdomain or on a portion of the boundary. We prove that the system is null controllable when the nonlinear term f(s) grows slower than s . log|s| as |s| → ∞.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Dubova, Anna Fernández-Cara, Enrique and González-Burgos, Manuel 1998. Controllability results for discontinuous semilinear parabolic partial differential equations. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 326, Issue. 12, p. 1391.

Zuazua, Enrique 1998. European Congress of Mathematics. p. 276.

Фурсиков, Андрей Владимирович Fursikov, Andrei Vladimirovich Эмануилов, Юрий Сергеевич and Emanuilov, Yurii Sergeevich 1999. Точная управляемость уравнений Навье - Стокса и Буссинеска. Успехи математических наук, Vol. 54, Issue. 3, p. 93.

Albano, Paolo Cannarsa, Piermarco and Komornik, Vilmos 1999. Optimal Control of Partial Differential Equations. p. 1.

Aniţa, Sebastian and Barbu, Viorel 2000. Null controllability of nonlinear convective heat equations. ESAIM: Control, Optimisation and Calculus of Variations, Vol. 5, Issue. , p. 157.

Teresa, Luz de 2000. Insensitizing controls for a semilinear heat equation. Communications in Partial Differential Equations, Vol. 25, Issue. 1-2, p. 39.

Rosier, Lionel 2000. Exact Boundary Controllability for the Linear Korteweg--de Vries Equation on the Half-Line. SIAM Journal on Control and Optimization, Vol. 39, Issue. 2, p. 331.

Khapalov, Alexander 2001. Exact null-controllability for the semilinear heat equation with superlinear term and mobile internal controls. Nonlinear Analysis: Theory, Methods & Applications, Vol. 43, Issue. 6, p. 785.

Khapalov, Alexander 2001. Mobile Point Controls Versus Locally Distributed Ones for the Controllability of the Semilinear Parabolic Equation. SIAM Journal on Control and Optimization, Vol. 40, Issue. 1, p. 231.

Zuazua, Enrique 2001. Carleman Estimates and Applications to Uniqueness and Control Theory. p. 191.

Yu. Imanuvilov, O and Yamamoto, M 2001. Control Of Nonlinear Distributed Parameter Systems.

Doubova, Anna Osses, A. and Puel, J.-P. 2002. Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients. ESAIM: Control, Optimisation and Calculus of Variations, Vol. 8, Issue. , p. 621.

Fernández-Cara, E. and Zuazua, E. 2002. Nonlinear PDE’s in Condensed Matter and Reactive Flows. p. 127.

Barbu, Viorel 2002. Local controllability of the phase field system. Nonlinear Analysis: Theory, Methods & Applications, Vol. 50, Issue. 3, p. 363.

Khapalov, A.Y. 2002. Mobile point controls versus the locally distributed ones for the controllability of the semilinear parabolic equation. Vol. 3, Issue. , p. 3384.

Doubova, A. Fernández-Cara, E. González-Burgos, M. and Zuazua, E. 2002. On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient. SIAM Journal on Control and Optimization, Vol. 41, Issue. 3, p. 798.

Khapalov, Alexander Y. 2002. Global non-negative controllability of the semilinear parabolic equation governed by bilinear control. ESAIM: Control, Optimisation and Calculus of Variations, Vol. 7, Issue. , p. 269.

Wang, Lijuan and Wang, Gengsheng 2003. The Optimal Time Control of A Phase-Field System. SIAM Journal on Control and Optimization, Vol. 42, Issue. 4, p. 1483.

Khodja, F. Ammar Benabdallah, A. Dupaix, C. and Kostin, I. 2003. Controllability to the Trajectories of Phase-Field Models by One Control Force. SIAM Journal on Control and Optimization, Vol. 42, Issue. 5, p. 1661.

Mahmudov, Nazim I. 2003. Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces. SIAM Journal on Control and Optimization, Vol. 42, Issue. 5, p. 1604.

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Null controllability of the semilinear heat equation

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Null controllability of the semilinear heat equation

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