Null controllability of a nonlinear diffusion system in reactor dynamics

Sakthivel, Kumarasamy ; Balachandran, Krishnan ; Park, Jong-Yeoul ; Devipriya, Ganeshan

Kybernetika, Tome 46 (2010) no. 5, pp. 890-906

Abstract (VO)

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.

Détail

Classification : 93B05, 93B07
Keywords: controllability; observability; parabolic integrodifferential equation

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