Null controllability of a population dynamics with interior degeneracy

In this paper, we deal with the null controllability of a population dynamics model with an interior degenerate diffusion. To this end, we proved first a new Carleman estimate for the full adjoint system and afterwards we deduce a suitable observability inequality which will be needed to establish the existence of a control acting on a subset of the space which lead the population to extinction in a finite time

Null controllability of a coupled model in population dynamics

summary:We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the ``gene type'' of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed by one control force. To reach our goal, we develop first a Carleman type inequality for its adjoint system and consequently the pertinent observability inequality. Note that such a system is obtained via the original paradigm using the Lagrangian method. Afterwards, with the help of a cost function we will be able to deduce the existence of a control acting on a subset of the gene type domain and which steers both populations of a certain class of age to extinction in a finite time.\looseness -

Null controllability of a cascade model in population dynamics

In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one control force. We develop first a Carleman type inequality for its adjoint system, and then an observability inequality which allows us to deduce the existence of a control acting on a subset of the space domain which steers both populations of a certain age to extinction in a finite time

Null controllability of a population dynamics with degenerate diffusion

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