Controllability for a parabolic equation with a nonlinear term involving the state and the gradient

Xu, Youjun; Liu, Zhenhai

doi:10.1016/s0252-9602(10)60152-x

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“…[5,6,7,8,9]). For the non-linear case, we can cite [10,11,12]. The present work is an extension of the recent paper [9], in which the null controllability of a reaction-diffusion system was solved under a finite number of contraints on the state.…”

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confidence: 98%

Simultaneous null controllability of parabolic equations with nonlocal terms

Louis-Rose

2017

2017 Proceedings of the Conference on Control and Its Applications

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This paper is concerned with a null controllability problem for nonlinear parabolic equations appearing in mathematical biology. We consider a system of two equations with a nonlocal nonlinearity, in a bounded domain Ω of R N 0 , N0 being a positive integer sufficiently small. Such models can be used in the context of dynamics of biological systems to describe the migration of population (of bacteria in a container). Our aim is to find a control common to both equations, which solves the null controllabillity of the studied system under constraints on the state. A similar control problem has recently been addressed for the Laplace operator, so the present paper extends those results.

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