Geodesic
Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1207-1224

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We discuss several new results on nonnegative approximate controllability for the one-dimensional Heat equation governed by either multiplicative or nonnegative additive control, acting within a proper subset of the space domain at every moment of time. Our methods allow us to link these two types of controls to some extend. The main results include approximate controllability properties both for the static and mobile control supports.

DOI : 10.1051/cocv/2012004
Classification : 35K05, 35K20, 93B05
Keywords: parabolic equation, approximate controllability, multiplicative controls, nonnegative locally distributed controls 
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     author = {Fern\'andez, Luis Alberto and Khapalov, Alexander Yuri},
     title = {Controllability properties for the one-dimensional {Heat} equation under multiplicative or nonnegative additive controls with local mobile support},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1207--1224},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {4},
     year = {2012},
     doi = {10.1051/cocv/2012004},
     mrnumber = {3019478},
     zbl = {1262.35119},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012004/}
}
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Fernández, Luis Alberto; Khapalov, Alexander Yuri. Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1207-1224. doi: 10.1051/cocv/2012004

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