In this article, we describe an optimal control strategy for sha** a large-scale swarm of
particles using boundary global actuation. This problem arises as a key challenge in many …

We present a new proof of the turnpike property for nonlinear optimal control problems,
when the running target is a steady control-state pair of the underlying system. Our strategy …

The goal of the present article is to study controllability properties of mixed systems of linear
parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one …

Let us consider a nonlinear degenerate reaction-diffusion equation with application to
climate science. After proving that the solution remains nonnegative at any time, when the …

This paper concerns the null control of quasi-linear parabolic systems where the diffusion
coefficient depends on the gradient of the state variable. In our main theoretical result, with …

One proves the exact controllability of the Fokker--Planck equation \rho_t-\frac12\Delta(uρ)-
div(bρ)=0, ρ(0)=\rho_0, ρ(T)=\rho_1, on a bounded domain O with reflecting conditions on …

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$$\begin {aligned}\begin {array}{ll}\rho _t-\Delta\beta (\rho)+{\mathrm {div}}(u\rho)= 0\\text
{in}(0,{\infty})\times {\mathbb {R}}^ d,\\\rho (0, x)=\rho _0 (x),\x\in {\mathbb {R}}^ d,\end …

These lecture notes address the controllability under state constraints of reaction-diffusion
equations arising in socio-biological contexts. We restrict our study to scalar equations with …

In this paper we consider the Boussinesq system with homogeneous Dirichlet boundary
conditions and defined in a regular domain Ω⊂ R^ N for N= 2 and N= 3. The …