Geodesic
Null controllability of a nonlinear diffusion system in reactor dynamics
Kybernetika, Tome 46 (2010) no. 5, pp. 890-906.

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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 $\mathbb R$ 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. Then this result is successfully used with some estimates for parabolic equation in $L^k$ spaces together with classical fixed point theorem, to prove the null controllability of the nonlinear model.
Classification : 93B05, 93B07
Keywords: controllability; observability; parabolic integrodifferential equation 
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     author = {Sakthivel, Kumarasamy and Balachandran, Krishnan and Park, Jong-Yeoul and Devipriya, Ganeshan},
     title = {Null controllability of a nonlinear diffusion system in reactor dynamics},
     journal = {Kybernetika},
     pages = {890--906},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2010},
     mrnumber = {2778922},
     zbl = {1205.93024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_5_a5/}
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Sakthivel, Kumarasamy; Balachandran, Krishnan; Park, Jong-Yeoul; Devipriya, Ganeshan. Null controllability of a nonlinear diffusion system in reactor dynamics. Kybernetika, Tome 46 (2010) no. 5, pp. 890-906. http://geodesic.mathdoc.fr/item/KYB_2010__46_5_a5/