Related papers: Global exponential stabilisation for the Burgers e…
This document provides a proof that the solutions to the convectively filtered Burgers equation, will converge to the entropy solution of the inviscid Burgers equation when certain restrictions are put on the initial conditions. It does so…
While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have…
In solving the problem of asymptotic tracking and disturbance rejection, it has been long always assumed that the reference to be tracked and the disturbance to be rejected must be generated by an exosystem such as a finite dimensional…
We consider a one dimensional transport equation with varying vector field and a small viscosity coefficient, controlled by one endpoint of the interval. We give upper and lower bounds on the minimal time needed to control to zero,…
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…
In this paper, we establish the existence and uniqueness of solutions to the two-dimensional Burgers equation using the framework of infinite-dimensional dynamical systems. The two-dimensional Burgers equation, which models the interplay…
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 address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
This paper is devoted to the study of the rapid exponential stabilization problem for a controlled Korteweg-de Vries equation on a bounded interval with homogeneous Dirichlet boundary conditions and Neumann boundary control at the right…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved earlier that if the random force is proportional to the square root of the viscosity,…
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…
We prove the control and stabilization of the Benjamin-Ono equation in $L^2(\T)$, the lowest regularity where the initial value problem is well-posed. This problem was already initiated in \cite{LinaresRosierBO} where a stronger…
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…
A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related regularisation of the shallow water system recently introduced by Clamond and Dutykh, the new regularisation…
In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness…
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approach introduced by Agrachev and Sarychev.…
A special initial condition for (1+1)-dimensional Burgers equation is considered. It allows to obtain new analytical solutions for an arbitrary low viscosity as well as for the inviscid case. The viscous solution is written as a rational…
This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…