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This paper investigates the existence and uniqueness of mild solutions, as well as the approximate controllability, of a class of fractional evolution equations with nonlocal conditions in Hilbert spaces. Sufficient conditions for…
We deal with the 3D Navier-Stokes equation in a smooth simply connected bounded domain, with controls on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the remaining, uncontrolled, part of the…
In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
In the present contribution we consider a singular phase field system located in a smooth and bounded three-dimensional domain. The entropy balance equation is perturbed by a logarithmic nonlinearity and by the presence of an additional…
We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent…
Because splashing is such a violent process, one might naively expect that neither the direction of droplet emission nor the amount of ejected material can be controlled with any precision. Even though it is observed countless times in the…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
A widely used stochastic plate equation is the classical plate equation perturbed by a term of It\^o's integral. However, it is known that this equation is not exactly controllable even if the controls are effective everywhere in both the…
In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…
This paper presents sufficient conditions for small-time local controllability of a control-affine system that describes the rotational motion of a satellite in a circular orbit. The satellite is modeled as a rigid body subject to…
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…
In this paper, we study the null and approximate controllability of a class of fully nonlocal coupled stochastic reaction--convection--diffusion systems. The system consists of two forward stochastic parabolic equations driven by general…
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control.…
The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a…
In this study, we study the null controllability of a multi-dimensional degenerate parabolic equation characterized by a degenerate interior point. The control domain, which is an arbitrary inner region, does not encompass the degenerate…
In this paper, we study the exact controllability and stabilization of a system of two wave equations coupled by velocities with an internal, local control acting on only one equation. We distinguish two cases. In the first one, when the…
We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…
We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the "follower players"…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…