Related papers: Controllability for a population equation with int…
In this work, we prove a Carleman estimate for a parabolic problem which has a dissipative degenerate term. The prove relies on choose a suitable weight function that change of sign inside the control domain.
We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
In this paper we present a null controllability result for a degenerate semilinear parabolic equation with first order terms. The main result is obtained after the proof of a new Carleman inequality for a degenerate linear parabolic…
We introduce a formula for the disagreement function which is used to control a recently proposed dynamics of the Ising spin system. This leads to four different phases of the Ising spin chain in a zero temperature. One of these phases is…
In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system…
In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. Here, we have a partially unknown data of the system, and the problem consists in finding…
This paper is devoted to the study of the internal null-controllability of the Grushin equation. We determine the minimal time of controllability for a large class of non-rectangular control region. We establish the positive result thanks…
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…
We consider systems of parabolic equations coupled in zero order terms in a star-like or a tree-like shape, with an internal control acting in only one of the equations. We obtain local exact controllability to the stationary solutions of…
In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We…
We consider the null-controllability problem for the generalized Baouendi-Grushin equation $(\partial_t - \partial_x^2 - q(x)^2\partial_y^2)f = 1_\omega u$ on a rectangular domain. Sharp controllability results already exist when the…
We consider a degenerate wave equation with drift in presence of a leading operator which is not in divergence form. We provide some conditions for the boundary controllability of the associated Cauchy problem.
We investigate the internal controllability of the wave equation with structural damping on the one dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove…
This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a…
We consider a linear nonlocal heat equation in a bounded domain $\Omega\subset\mathbb{R}^d$ with Dirichlet boundary conditions. The non-locality is given by the presence of an integral kernel. We analyze the problem of controllability when…
We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we…
We consider the linear degenerate wave equation, on the interval $(0, 1)$ $$ w_{tt} - (x^\alpha w_x)_x = p(t) \mu (x) w, $$ with bilinear control $p$ and Neumann boundary conditions. We study the controllability of this nonlinear control…
A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely…