Related papers: Closed-loop control of a reaction-diffusion system
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…
The distributed null controllability for coupled parabolic systems with non-diagonalizable diffusion matrices with a reduced number of controls has been studied in the case of constant matrices. On the other hand, boundary controllability…
Feedback or closed-loop control allows dynamical systems to increase their performance up to a limit imposed by the second law of thermodynamics. It is expected that within this limit, the system performance increases as the controller uses…
In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate reaction-diffusion equation in divergence…
Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to specific molecules. The corresponding boundary conditions,…
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be…
An explicit output-feedback boundary feedback law is introduced that stabilizes an unstable linear constant-coefficient reaction-diffusion equation on an $n$-ball (which in 2-D reduces to a disk and in 3-D reduces to a sphere) using only…
The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
In this paper, we consider a nonlinear system of two parabolic equations, with a distributed control in the first equation and an odd coupling term in the second one. We prove that the nonlinear system is small-time locally…
We consider a nonlinear reaction diffusion system of parabolic type known as the monodomain equations, which model the interaction of the electric current in a cell. Together with the FitzHugh-Nagumo model for the nonlinearity they…
The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically,…
We consider the output-feedback stabilization of a one-dimensional cascade coupling a reaction-diffusion equation and a wave equation through an internal term, with Neumann boundary control acting at the wave endpoint. Two measurements are…
Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point. This fixed-point becomes…
Motivated by the possibility of electrochemical control of phase separation, a variational theory of thermodynamic stability is developed for driven reactive mixtures, based on a nonlinear generalization of the Cahn-Hilliard and Allen-Cahn…
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 note shows how classical tools from linear control theory can be leveraged to provide a global analysis of nonlinear reaction-diffusion models. The approach is differential in nature. It proceeds from classical tools of contraction…
This paper deals with a parabolic-elliptic chemotaxis system with nonlinear diffusion. It was proved that there exists a solution of a Cahn-Hilliard system as an approximation of a nonlinear diffusion equation by applying an abstract theory…
We discuss equivalent formulations of the control of conditional processes introduced by Lions. In this problem, a controlled diffusion process is killed once it hits the boundary of a given domain and the controller's reward is computed…