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This paper is devoted to the theoretical and numerical analysis of the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the ODE-heat with distributed control using Carleman estimates. Then, we conclude by the strategy of space domain extension. Finally, we illustrate the analysis with some numerical experiments.

This paper aims to address an interesting open problem posed in the paper ''Singular Optimal Control for a Transport-Diffusion Equation'' of Sergio Guerrero and Gilles Lebeau in 2007. The problem involves studying the null-controllability cost of a transport-diffusion equation with Neumann conditions. Our objective is twofold. Firstly, we investigate the scenario where each trajectory of the tangential velocity enters the control region in a shorter time at a fixed entry time. By employing Agmon inequalities and Carleman estimates, we establish that the control cost remains bounded for sufficiently small diffusivity and large control time. Secondly, we explore the case where at least one trajectory fails to enter the control region. In this scenario, we prove that the control cost explodes exponentially when the diffusivity approaches zero and the control time is sufficiently small.

We consider a degenerate wave equation with drift in presence of a leading operator which is not in divergence form. We provide some conditions for the boundary controllability of the associated Cauchy problem., Comment: 25 pages

This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.

In this paper we consider a cascade system in non divergence form which models the interaction between two different species, the first one can be seen as a predator and the other as a prey. Both of them depend on time, on age and on space. Moreover, the diffusion coefficients degenerate at the boundary of domain. We study, in particular, null controllability of the system via the observability inequality for the non homogeneous adjoint problem, which is deduced by Carleman estimates., Comment: arXiv admin note: text overlap with arXiv:1701.04083 by other authors

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.

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established., Comment: Accepted in J. Anal. Math. arXiv admin note: text overlap with arXiv:1508.04014