Related papers: Unique Continuation for Fifth-Order KP Equation an…
We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equa- tion on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet boundary conditions at the end-points…
In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the…
Studied here is the Kawahara equation, a fifth order Korteweg-de Vries type equation, with time-delayed internal feedback. Under suitable assumptions on the time delay coefficients we prove that solutions of this system are exponentially…
This paper presents a method to verify closed-loop properties of optimization-based controllers for deterministic and stochastic constrained polynomial discrete-time dynamical systems. The closed-loop properties amenable to the proposed…
The article studies the exact controllability and the stability of the sixth order Boussinesq equation \[ u_{tt}-u_{xx}+\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \quad \beta=\pm1, \] on the interval $S:=[0,2\pi]$ with periodic boundary…
The method of nonlinear self-adjointness is applied to the Kadomtsev-Petviashvili equation. The infinite set of conservation laws associated with the infinite algebra of Lie point symmetry of the KP equation is constructed.
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…
This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous…
We propose and analyze a new dynamical system with a closed-loop control law in a Hilbert space $\mathcal{H}$, aiming to shed light on the acceleration phenomenon for \textit{monotone inclusion} problems, which unifies a broad class of…
In this paper, we study the indirect boundary stability and exact controllability of a one-dimensional Timoshenko system. In the first part of the paper, we consider the Timoshenko system with only one boundary fractional damping. We first…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
The aim of this paper is the accurate numerical study of the KP equation. In particular we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end we first study…
We report the local-in-time conservative dynamics of nonspinning binary systems at fifth Post-Minkowskian (5PM) and first self-force (1SF) orders. This follows from an explicit calculation of the 5PM/1SF nonlocal-in-time tail-type…
We propose to explore switching methods in order to recover some properties of Kalmanlike observers for output feedback stabilization of state-affine systems that may present observability singularities. The self-tuning gain matrix in…
In this paper we propose a new observability property for nonautonomous linear control systems in finite dimension; the nonuniform complete observability, which is more general than the uniform complete observability. The main result of…
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
We study in this paper boundary stabilization, in the L2 sense, of the perturbed Kuramoto-Sivashinsky (KS) equation subject to intermittent sensing. We assume that we measure the state on a given spatial subdomain during certain time…