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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 7, page 269-283
- ISSN: 1292-8119

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topKhapalov, Alexander Y.. "Global non-negative controllability of the semilinear parabolic equation governed by bilinear control." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 269-283. <http://eudml.org/doc/90622>.

@article{Khapalov2010,

abstract = {
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 traditional additive controls of localized support is out of question. However, we will show that a system like that can be steered in L²(0,1) from any non-negative nonzero initial state into any neighborhood of any desirable non-negative target state by at most three static (x-dependent only) above-mentioned bilinear controls, applied subsequently in time, while only one such control is needed in the linear case.
},

author = {Khapalov, Alexander Y.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Semilinear parabolic equation; global approximate controllability; bilinear control.; semilinear parabolic equation; bilinear system; reachability},

language = {eng},

month = {3},

pages = {269-283},

publisher = {EDP Sciences},

title = {Global non-negative controllability of the semilinear parabolic equation governed by bilinear control},

url = {http://eudml.org/doc/90622},

volume = {7},

year = {2010},

}

TY - JOUR

AU - Khapalov, Alexander Y.

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 7

SP - 269

EP - 283

AB -
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 traditional additive controls of localized support is out of question. However, we will show that a system like that can be steered in L²(0,1) from any non-negative nonzero initial state into any neighborhood of any desirable non-negative target state by at most three static (x-dependent only) above-mentioned bilinear controls, applied subsequently in time, while only one such control is needed in the linear case.

LA - eng

KW - Semilinear parabolic equation; global approximate controllability; bilinear control.; semilinear parabolic equation; bilinear system; reachability

UR - http://eudml.org/doc/90622

ER -

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