Displaying similar documents to “Optimal blowup rates for the minimal energy null control of the strongly damped abstract wave equation”

An output controllability problem for semilinear distributed hyperbolic systems

E. Zerrik, R. Larhrissi, H. Bourray (2007)

International Journal of Applied Mathematics and Computer Science

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The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated...

Exact controllability of the radial solutions of the semilinear wave equation in R.

Luz de Teresa (1998)

Revista Matemática Complutense

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The exact internal controllability of the radial solutions of a semilinear heat equation in R is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.

Some new results related to the null controllability of the 1 - d heat equation

Antonio López, Enrique Zuazua (1997-1998)

Séminaire Équations aux dérivées partielles

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We address three null controllability problems related to the 1 - d heat equation. First we show that the 1 - d heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also prove that the same result holds for the finite-difference semi-discretization in space of the constant coefficient heat equation as the step size tends to zero. Finally, we prove that the null controllability of the constant coefficient heat equation...

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...