Displaying similar documents to “Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type”

Null controllability of a nonlinear diffusion system in reactor dynamics

Kumarasamy Sakthivel, Krishnan Balachandran, Jong-Yeoul Park, Ganeshan Devipriya (2010)

Kybernetika

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In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of ℝ with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients....

Global non-negative controllability of the semilinear parabolic equation governed by bilinear control

Alexander Y. Khapalov (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain via the coefficient (bilinear control) in the additive reaction term. Clearly, even in the linear case, due to the maximum principle, such system is not globally or locally controllable in any reasonable linear space. It is also well known that for the superlinear terms admitting a power growth at infinity the global approximate controllability...

Exact controllability of linear dynamical systems: A geometrical approach

María Isabel García-Planas (2017)

Applications of Mathematics

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In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that...

Null-controllability of some systems of parabolic type by one control force

Farid Ammar Khodja, Assia Benabdallah, Cédric Dupaix, Ilya Kostin (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the null controllability by one control force of some linear systems of parabolic type. We give sufficient conditions for the null controllability property to be true and, in an abstract setting, we prove that it is not always possible to control.

Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case

Enrique Fernández-Cara, Manuel González-Burgos, Sergio Guerrero, Jean-Pierre Puel (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form ∂ y ∂ n + f ( y ) = 0 . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear,...