Related papers: Stabilization and approximate null-controllability…
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…
In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
In this article, we prove null-controllability results for the heat equation associated tofractional Baouendi-Grushin operators $$\partial_t u+\bigl(-\Delta_x-V(x)\Delta_y\bigr)^s u= \mathbb{1}_\Omega h$$ where $V$ is a potential that…
We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term $V(x)u,$ a nonlinear term of the form $\mathrm{i}\mu…
We consider the problem of stabilization to zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum. This problem was previously studied in…
Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the…
This paper is concerned with the constrained approximate null controllability of heat equation coupled by a real matrix $P$, where the controls are impulsive and periodically acted into the system through a series of real matrices…
We consider the semilinear heat equation posed on a smooth bounded domain $\Omega$ of $\mathbb{R}^{N}$ with Dirichlet or Neumann boundary conditions. The control input is a source term localized in some arbitrary nonempty open subset…
This paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair (A,B) of constant matrices. We present a necessary and sufficient condition for the approximate controllability,…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
We study the regularity of the bounded self-similar solution to the one-phase Stefan problem with fractional diffusion posed on the whole line. In terms of the enthalpy $h(x,t)$, the evolution problem reads \[ \begin{cases} \partial_t h +…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, t, u) - u_t \ge f (x, t) g (u) \quad \mbox{in} {\mathbb R}_+^{n+1} = {\mathbb R}^n \times…
In this note, we give an elementary proof of the lack of null controllability for the heat equation on the half line by employing the machinery inherited by the unified transform, known also as the Fokas method. This approach also extends…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally…
We prove new bounds on the control cost for the abstract heat equation, assuming a spectral inequality or uncertainty relation for spectral projectors. In particular, we specify quantitatively how upper bounds on the control cost depend on…
In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and…