Related papers: Stabilization by switching control methods
This paper studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
The paper deals with initial-boundary value problems for the linear wave equation whose solutions stabilize to zero in a finite time. We prove that problems in this class remain exponentially stable in $L^2$ as well as in $C^2$ under small…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We investigate the evolution of dispersive waves governed by linear wave equations, where a finite duration source is applied. The resulting wave may be viewed as the superposition of modes before the source is turned on and after it is…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…
This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…
The evolution problem for a quantum particle confined in a 1D box and interacting with one fixed point through a time dependent point interaction is considered. Under suitable assumptions of regularity for the time profile of the…
In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$ of the one-dimensional nonlinear damped wave equation with a localized damping and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by…
This thesis aims at investigating the first steps toward an unconditionally stable space-time isogeometric method, based on splines of maximal regularity, for the linear acoustic wave equation. The unconditional stability of space-time…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
We consider a stabilization problem for a piezoelectric system. We prove an exponential stability result under some Lions geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate…
In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with…
This paper investigates inverse potential problems of wave equations with cubic nonlinearity. We develop a methodology for establishing stability estimates for inversion of lower order coefficients. The new ingredients of our approach…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
We investigate trend to equilibrium for the damped wave equation with a confining potential in the Euclidean space. We provide with necessary and sufficient geometric conditions for the energy to decay exponentially uniformly. The proofs…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…