Related papers: Control of the half-heat equation

We study the internal non null-controllability properties of the heat equation on 2-dimensional almost-Riemannian manifolds with an interior singularity, and under the assumption that the closure of the control zone does not contain the…

We study the memory-type null controllability property for wave equations involving memory terms. The goal is not only to drive the displacement and the velocity (of the considered wave) to rest at some time-instant but also to require the…

We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete…

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…

The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution…

This paper deals with the approximate controllability for the semilinear heat equation in one space dimension. Our aim is to provide an estimate of the cost of the control.

This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is…

We study the null-controllability of parabolic equations associated to a general class of hypoelliptic quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued…

In this paper, we consider forward stochastic nonlinear parabolic equations, with a control localized in the drift term. Under suitable assumptions, we prove the small-time global null-controllability, with a truncated nonlinearity. We also…

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…

We consider the Kawahara equation, a fifth order Korteweg-de Vries type equation, posed on a bounded interval. The first result of the article is related to the well-posedness in weighted Sobolev spaces, which one was shown using a general…

Partial differential equation on networks have been widely investigated in the last decades in view of their application to quantum mechanics (Schr\"odinger type equations) or to the analysis of flexible structures (wave type equations).…

In this paper, we establish some important results for the impulsive wave equation. We begin by proving the existence of a solution. Then, we study the impulse approximate controllability where the control function acts on a subdomain…

In this article, we study the null-controllability and observability properties of a bi-dimensio\-nal fluid-structure interaction system, governed by the heat equation coupled with the damped beam equation. To do so, we prove a global…

We discuss reachable states for the Hermite heat equation on a segment with boundary $L^2$-controls. The Hermite heat equation corresponds to the heat equation to which a quadratic potential is added. We will discuss two situations: when…

We demonstrate that the time-dependent projected Gross-Pitaevskii equation derived earlier [Davis, et al., J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. We find that this…

We study quantum control of the full hyperfine manifold in the ground-electronic state of alkali atoms based on applied radio frequency and microwave fields. Such interactions should allow essentially decoherence-free dynamics and the…

Flatness-based control design is a well established method to generate open-loop control signals. Several articles discuss the application of flatness-based control design of (reaction-) diffusion problems for various scenarios. Beside the…

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…

The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…