Related papers: Averaged controllability for random evolution part…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…
We prove controllability results for abstract systems of weakly coupled $N$ evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N-1$ controls. We give applications to…
The paper addresses the study of a class of evolutionary quasi-variational inequalities of the parabolic type arising in the formation and growth models of granular and cohensionless materials. Such models and their mathematical…
In this paper we introduce a new dynamical condition, the comb geometric control condition, which is sufficient for observability of the Schr\"odinger equation in Euclidean space. We provide examples which show this condition is strictly…
We prove the interior and boundary null-controllability of some parabolic evolutions with controls acting over measurable sets.
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we…
We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.
We consider a controlled Schr\"odinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We…
It is by now well known that the use of Carleman estimates allows to establish the control-lability to trajectories of nonlinear parabolic equations. However, by this approach, it is not clear how to decide whether a given function is…
In this paper, we are concerned with the boundary controllability of heat equation with dynamic boundary conditions. More precisely, we prove that the equation is null controllable at any positive time by means of a boundary control…
We present the random behaviour of the Schr\"odinger map equation, a geometric partial differential equation, by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results obtained are…
In many practical applications of control theory some constraints on the state and/or on the control need to be imposed. In this paper, we prove controllability results for semilinear parabolic equations under positivity constraints on the…
We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
We study several controllability properties for some semilinear parabolic PDE with a quadratic gradient term. For internal distributed controls, it is shown that the system is approximately and null controllable. The proof relies on the…
We study controllability of $d$-dimensional defocusing cubic Schroedinger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes)…
This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…