Boundary Sentinel with Given Sensitivity in Population Dynamics Problem and Parameters Identification

Mifiamba Soma, Somdouda Sawadogo

Abstract

The notion of sentinels with given sensitivity was introduced by J.L.Lions [11] in order to identify parameters in the problem of pollution ruled by a parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. In population dynamics model, we reconsider this notion of sentinels in a more general framework. We prove the existence of the boundary sentinels by solving a boundary
null-controllability problem with constraint on the control. Our results use Carleman inequality which is adapted to the constraint.

Keywords

population dynamics, optimal control, controllability, sentinels, Carleman inequality.

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