相关论文: Global Stabilization of BBM-Burgers' Type Equation…
In this article, global stabilization results for the two dimensional (2D) viscous Burgers' equation, that is, convergence of unsteady solution to its constant steady state solution with any initial data, are established using a nonlinear…
Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers'…
This paper presents a global stabilization result of the viscous Burgers' equation with the memory term by applying Neumann boundary feedback control laws. We construct suitable feedback control inputs using the control Lyapunov functional…
This article focuses on a nonlinear Neumann boundary feedback control formulation for the viscous Burgers' equation and develops a class of finite difference schemes to achieve global stabilization. The proposed procedure, known as the…
We study the problem of global exponential stabilization of original Burgers' equations and the Burgers' equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the…
In this article, we explore the feedback stabilization of a viscous Burgers equation around a non-constant steady state using localized interior controls and then develop error estimates for the stabilized system using finite element…
In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping…
In this article, we investigate a generalized Burgers-Huxley equation with a smooth kernel defined in a bounded domain $\Omega\subset\mathbb{R}^d$, $d\in\{1,2,3\}$, focusing on feedback stabilizability around a non-constant steady state.…
In this article, we develop a fully discrete numerical scheme for the one-dimensional (1D) and two-dimensional (2D) viscous Burgers equations with nonlinear Neumann boundary feedback control. The temporal discretization employs a…
In this paper, we study a generalized Burgers-Huxley equation with memory, subject to nonhomogeneous Dirichlet boundary conditions. We construct a linear, finite-dimensional Dirichlet boundary feedback controller aimed at stabilizing the…
In this work, a boundary control problem for the following generalized Burgers-Huxley (GBH) equation: $$u_t=\nu u_{xx}-\alpha u^{\delta}u_x+\beta u(1-u^{\delta})(u^{\delta}-\gamma), $$ where $\nu,\alpha,\beta>0,$ $1\leq\delta<\infty$,…
We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global wellposedness of…
In the paper, a newly developed three-point fourth-order compact operator is utilized to construct an efficient compact finite difference scheme for the Benjamin-Bona-Mahony-Burgers' (BBMB) equation. Detailed derivation is carried out based…
This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error…
The aim of this work is to design an explicit finite dimensional boundary feedback controller of sampled-data form for locally exponentially stabilizing the equilibrium solutions to semilinear parabolic equations. The feedback controller is…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
This article is intended to present a qualitative and numerical analysis of well-posedness and boundary stabilization problems of the well-known Korteweg-de Vries-Burgers equation. Assuming that the boundary control is of memory type, the…
The aim of this paper is to study the controllability and stabilization for the Benjamin equation on a periodic domain $\mathbb{T}$. We show that the Benjamin equation is globally exactly controllable and globally exponentially stabilizable…
We describe a general multiplier method to obtain boundary stabilization of the wave equation by means of a (linear or quasi-linear) Neumann feedback. This also enables us to get Dirichlet boundary control of the wave equation. This method…
In this paper, we focus on the rapid boundary stabilization of 1D nonlinear parabolic equations via the modal decomposition method. The nonlinear term is assumed to satisfy certain local Lipschitz continuity and global growth conditions.…