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The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the…
We consider an initial boundary value problem for a quantum version of the Zakharov system arising in plasma physics. We prove the global well-posedness of this problem in some Sobolev type classes and study properties of solutions. This…
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…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
We consider the stabilisation of solutions to the Cahn-Hilliard equation towards a given trajectory by means of a finite-dimensional static output feedback mechanism. Exponential stabilisation of the controlled state around the target…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of various classes of damped nonlinear wave equations. Specifically, stabilization the zero steady state solution of initial boundary value…
We propose a novel framework for stabilization, with an estimate of the region of attraction, of quasilinear parabolic partial differential equations (PDEs) that exhibit finite-time blow-up phenomena when null boundary inputs are imposed.…
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
In this paper, we consider a damped Navier-Stokes-Bardina model posed on the whole three-dimensional. These equations have an important physical motivation and they arise from some oceanic model. From the mathematical point of view, they…
In this paper, we are concerned with the one-dimensional initial boundary value problem for isentropic gas dynamics. Through the contribution of great researchers such as Lax, P. D., Glimm, J., DiPerna, R. J. and Liu, T. P., the decay…
This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
Initial-boundary value problems for the 2D Zakharov-Kuznetsov equation posed on bounded rectangles and on a strip are considered. Spectral properties of a linearized operator and critical sizes of domains are studied. Exponential decay of…
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…
This paper is concerned with the long-time behavior of solutions for the three dimensional globally modified Navier-Stokes equations in a three-dimensional bounded domain. We prove the existence of a global attractor $\mathcal{A}_0$ in $H$…