相关论文: Stabilization for a degenerate wave equation with …

This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…

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…

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

In this paper we study the stabilization of rotating waves using time delayed feedback control. It is our aim to put some recent results in a broader context by discussing two different methods to determine the stability of the target…

In this paper, we are concerned with the large time behavior of viscous shock wave for the convective porous-media equation with degenerate viscosity. We get the regularity of the solution for general initial data and prove the shock wave…

This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population…

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…

In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…

We study the rate of decay of the energy functional of solutions of the wave equation with localized damping and a external force. We prove that the decay rates of the energy functional is determined from a forced differential equation.

The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…

We study the problem of stabilization for a class of evolution systems with fractional-damping. After writing the equations as an augmented system we prove in this article first that the problem is well posed. Second, using the LaSalle's…

This paper addresses the problem of exponential and accelerated finite-time, as well as nearly fixed-time, stabilization of switched linear MIMO systems. The proposed approach relies on a generalized homogenization framework for switched…

This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…

This work investigates the boundary stabilization problem of the Hirota-Satsuma system. In the problem under consideration, a boundary feedback law consisting of a linear combination of a damping mechanism and a time-delay term is designed.…

The problem of the exact bounded control of oscillations of the two-dimensional wave equation is considered. Control force is applied to the boundary of the membrane, which is located in a domain on a plane. The goal of the control is to…

We consider the wave equation with a damping term on a partially rectangular planar domain, assuming that the damping is concentrated close to the non-rectangular part of the domain. Polynomial decay estimates for the energy of the solution…

We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…

In this paper, we study the impulse controllability of a multi-dimensional heat equation with dynamic boundary conditions in a bounded smooth domain. Using a recent approach based on finite-time stabilization, we show that the system is…

One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…

We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…