Abstract
We first prove a new controllability result for a nonlinear two stroke system. The key to solve this controllability problem is an adapted Carleman inequality. Next, the obtained result is used to build a boundary sentinel to identify unknown parameters in a nonlinear population dynamics model with incomplete data.
Highlights
Let Ω ⊂ Rn, n ∈ {1, 2, 3} an open and bounded subset, with ∂Ω = Γ of class C∞
There exists a positive real weight function θ a precise definition of θ given by (13) such that, for any function h0 ∈ L2(U × O) with θh0 ∈ L2(U × O), there exists a unique control v ∈ K⊥ such that the pair (v, q) with q = q(v) is solution of the null boundary controllability problem with constraint on the control (34)-(36)
In view of (55), (56) and (57), (v, q) verifies the null controllability (34)-(36) and there exists a solution to the boundary null controllability problem
Summary
(Mercan & Mophou, 2014) proved a null controllability problem with constraints on the state for an adjoint system of population dynamics model. The following result hold: Theorem 4 Let Ω be a bounded open subset of Rn with boundary Γ of class C∞. There exists a positive real weight function θ a precise definition of θ given by (13) such that, for any function h0 ∈ L2(U × O) with θh0 ∈ L2(U × O), there exists a unique control v ∈ K⊥ such that the pair (v, q) with q = q(v) is solution of the null boundary controllability problem with constraint on the control (34)-(36). In view of (55), (56) and (57), (v, q) verifies the null controllability (34)-(36) and there exists a solution to the boundary null controllability problem It is clear from (40) that ρ satisfies.
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