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

Alexander Y. Khapalov — 2002

ESAIM: Control, Optimisation and Calculus of Variations

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 by...

Reachability of nonnegative equilibrium states for the semilinear vibrating string by varying its axial load and the gain of damping

Alexander Y. Khapalov — 2006

ESAIM: Control, Optimisation and Calculus of Variations

We show that the set of nonnegative equilibrium-like states, namely, like ( y d , 0 ) of the semilinear vibrating string that can be reached from any non-zero initial state ( y 0 , y 1 ) H 0 1 ( 0 , 1 ) × L 2 ( 0 , 1 ) , by varying its axial load and the gain of damping, is dense in the “nonnegative” part of the subspace L 2 ( 0 , 1 ) × { 0 } of L 2 ( 0 , 1 ) × H - 1 ( 0 , 1 ) . Our main results deal with nonlinear terms which admit at most the linear growth at infinity in y and satisfy certain restriction on their total impact on (0,∞) with respect to the time-variable.

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

Alexander Y. Khapalov — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We study the global approximate controllability of the one dimensional semilinear convection-diffusion-reaction equation governed in a bounded domain the coefficient () 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 by traditional additive...

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