相关论文: Stabilization and control of the nonlinear plate e…

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive…

It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…

We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and…

In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact…

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation with degeneracy and singularity occurring at the boundary of the spatial domain. Exact boundary controllability is proved in…

We discuss the stability properties of the solutions of the general nonlinear Schroedinger equation (NLSE) in 1+1 dimensions in an external potential derivable from a parity-time (PT) symmetric superpotential $W(x)$ that we considered…

Asymptotic-in-time feedback control of a panel interacting with an inviscid, subsonic flow is considered. The classical model [22] is given by a clamped nonlinear plate strongly coupled to a convected wave equation on the half space. In the…

This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…

The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the…

The aim of this work is to study the controllability of the bilinear Schr\"odinger equation on compact graphs. In particular, we consider the equation (BSE) $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space…

The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schr\"odinger equation and Klein-Gordon equation. These theories encompass both local and global well-posedness, as…

We prove that the geometric control condition is not necessary to obtain the smoothing effect and the uniform stabilization for the strongly dissipative Schr\"odinger equation.

This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an…

Discrete-time models of non-uniformly sampled nonlinear systems under zero-order hold relate the next state sample to the current state sample, (constant) input value, and sampling interval. The exact discrete-time model, that is, the…

This paper is devoted to the analysis of a semilinear suspension bridge model with pointwise localized dissipation. The main contribution of the work is the development of a robust semigroup framework that substantially simplifies the…

We consider Cauchy problem for the semilinear plate equation with nonlocal nonlinearity. Under mild conditions on the damping coefficient, we prove that the semigroup generated by this problem possesses a global attractor.

We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…

We investigate full Lipschitzian and full H\"olderian stability for a class of control problems governed by semilinear elliptic partial differential equations, where all the cost functional, the state equation, and the admissible control…

We consider the initial value problem for the semilinear plate equation with nonlocal nonlinearity. We prove the existence of global attractor and then establish the regularity and finite dimensionality of this attractor.

The elimination of aeroelastic instability (resulting in sustained oscillations of bridges, buildings, airfoils) is a central engineering and design issue. Mathematically, this translates to strong asymptotic stabilization of a 3D flow by a…