ISSN 21632480 (e)

Current volume

Journal archive


EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE's and FDEs. Topics include:
* Modeling of physical systems as infinitedimensional processes
* Direct problems such as existence, regularity and wellposedness
* Stability, longtime behavior and associated dynamical attractors
* Indirect problems such as exact controllability, reachability theory and inverse problems
* Optimization  including shape optimization  optimal control, game theory and calculus of variations
* Wellposedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s)
* Applications of the theory to physics, chemistry, engineering, economics, medicine and biology
The journal also welcomes excellent contributions on interesting and challenging ODE systems which arise as simplified models of infinitedimensional structures.
The journal adheres to the publication ethics and malpractice policies outlined by COPE.

TOP 10 Most Read Articles in EECT, August 2014
1 
Regularity and stability of a wave equation with a strong damping and dynamic boundary conditions
Volume 2, Number 4, Pages: 631  667, 2013
Nicolas Fourrier
and Irena Lasiecka
Abstract
References
Full Text
Related Articles
We present an analysis of regularity and stability of solutions corresponding to wave equation with dynamic boundary conditions. It has been known since the pioneering work by [26, 27, 30] that addition of dynamics to the boundary may change drastically both regularity and stability properties of the underlying system.
We shall investigate these properties in the context of wave equation with the damping affecting either the interior dynamics or the boundary dynamics or both.
This leads to a consideration of a wave equation acting on a bounded 3d domain coupled with another second order dynamics acting on the boundary. The wave equation is equipped with a viscoelastic damping, zero Dirichlet boundary conditions on a portion of the boundary and dynamic boundary conditions. These are general Wentzell type of boundary conditions which describe wave equation oscillating on a tangent manifold of a lower dimension.
We shall examine regularity and stability properties of the resulting system as a function of strength and location of the dissipation. Properties such as wellposedness of finite energy solutions, analyticity of the associated semigroup,
strong and uniform stability will be discussed.
The results obtained analytically are illustrated by numerical analysis. The latter shows the impact of various
types of dissipation on the spectrum of the generator as well as the dynamic behavior of the solution on a rectangular domain.

2 
On LandauLifshitz equations of noexchange energy models in ferromagnetics
Volume 2, Number 4, Pages: 599  620, 2013
Wei Deng
and Baisheng Yan
Abstract
References
Full Text
Related Articles
In this paper, we study LandauLifshitz equations of ferromagnetism with a total energy that does not include a socalled exchange energy. Many problems, including existence, stability, regularity and asymptotic behaviors, have been extensively studied for such equations of models with the exchange energy. The problems turn out quite different and challenging for LandauLifshitz equations of noexchange energy models because the usual methods based on certain compactness do not apply. We present a new method for the existence of global weak solution to the LandauLifshitz equation of noexchange energy models based on the existence of regular solutions for smooth data and certain stability of the solutions.
We also study higher time regularity, energy identity and asymptotic behaviors in some special cases for weak solutions.

3 
Boundary stabilization of
the NavierStokes equations with feedback controller via a Galerkin method
Volume 3, Number 1, Pages: 147  166, 2014
Evrad M. D. Ngom,
Abdou Sène
and Daniel Y. Le Roux
Abstract
References
Full Text
Related Articles
In this work we study the exponential stabilization of the two and threedimensional
NavierStokes equations in a bounded domain $\Omega$, around a given steadystate flow,
by means of a boundary control. In order to determine a feedback law, we consider an
extended system coupling the NavierStokes equations with an equation satisfied by the
control on the domain boundary. While most traditional approaches apply a feedback
controller via an algebraic Riccati equation, the StokesOseen operator or
extension operators, a Galerkin method is proposed instead in this study.
The Galerkin method permits to construct a stabilizing boundary control
and by using energy a priori estimation technics, the exponential decay is obtained.
A compactness result then allows us to pass to the limit in the system satisfied by
the approximated solutions. The resulting feedback control is proven to be globally
exponentially stabilizing the steady states of the two and threedimensional
NavierStokes equations.

4 
Existence and asymptotic behaviour for solutions of dynamical equilibrium systems
Volume 3, Number 1, Pages: 1  14, 2014
Zaki Chbani
and Hassan Riahi
Abstract
References
Full Text
Related Articles
In this paper, we give an existence result for the following dynamical equilibrium problem:
$\langle \frac{du}{dt},vu(t)\rangle+F(u(t),v)\geq 0 \;\; \forall v\in K $ and for $a.e. \;t \geq 0$, where $K$ is a closed convex set in a Hilbert space and $ F:K \times K \rightarrow \mathbb{R}$ is a monotone bifunction. We introduce a class of demipositive bifunctions and use it to study the asymptotic behaviour of
the solution $ u(t) $ when $ t\rightarrow\infty $. We obtain weak convergence of $ u(t) $ to some solution $x\in K$ of the equilibrium problem $F(x,y)\geq 0 $ for every $y\in K$. Our applications deal with the asymptotic behaviour of the dynamical convex minimization and dynamical system associated to saddle convexconcave bifunctions. We then present a new neural model for solving a convex programming problem.

5 
Carleman Estimates and null controllability of coupled degenerate systems
Volume 2, Number 3, Pages: 441  459, 2013
El Mustapha Ait Ben Hassi,
Farid Ammar khodja,
Abdelkarim Hajjaj
and Lahcen Maniar
Abstract
References
Full Text
Related Articles
In this paper, we study the null controllability of weakly degenerate
parabolic systems with two different diffusion coefficients and one control force.
To obtain this aim, we had to develop new global Carleman estimates for a
degenerate parabolic equation, with weight functions different from the ones of [2],
[10] and [31].

6 
Asymptotics for a second order differential equation with a linear, slowly timedecaying damping term
Volume 2, Number 3, Pages: 461  470, 2013
Alain Haraux
and Mohamed Ali Jendoubi
Abstract
References
Full Text
Related Articles
A gradientlike property is established for second order semilinear conservative systems in presence of a linear damping term which is asymptotically weak for large times. The result is obtained under the condition that the only critical points of the potential are absolute minima. The damping term may vanish on large intervals for arbitrarily large times and tends to $0$ at infinity, but not too fast (in a nonintegrable way). When the potential satisfies an adapted, uniform, Łojasiewicz gradient inequality, convergence to equilibrium of all bounded solutions is shown, with examples in both analytic and nonanalytic cases.

7 
A remark on Littman's method of boundary controllability
Volume 2, Number 4, Pages: 621  630, 2013
Matthias Eller
Abstract
References
Full Text
Related Articles
We extend the method of exact boundary controllability of strictly hyperbolic equations developed by W. Littman [22,23] to a large class of hyperbolic systems with constant coefficients. Our approach is based on the knowledge of the singularities of the fundamental solution of hyperbolic operators.

8 
Boundary approximate controllability of some linear parabolic systems
Volume 3, Number 1, Pages: 167  189, 2014
Guillaume Olive
Abstract
References
Full Text
Related Articles
This paper focuses on the boundary approximate controllability of two classes of linear parabolic systems, namely a system of $n$ heat equations coupled through constant terms and a $2 \times 2$ cascade system coupled by means of a first order partial differential operator with spacedependent coefficients.
For each system we prove a sufficient condition in any space dimension and we show that this condition turns out to be also necessary in one dimension with only one control.
For the system of coupled heat equations we also study the problem on rectangle, and we give characterizations depending on the position of the control domain.
Finally, we prove the distributed approximate controllability in any space dimension of a cascade system coupled by a constant first order term.
The method relies on a general characterization due to H.O. Fattorini.

9 
Stability analysis of nonlinear plates coupled with Darcy flows
Volume 2, Number 2, Pages: 193  232, 2013
Eugenio Aulisa,
Akif Ibragimov
and Emine Yasemen KayaCekin
Abstract
References
Full Text
Related Articles
In this paper we study the dynamical response of a nonlinear plate with viscous damping perturbed in both vertical and axial directions and interacting with Darcy flow. We first consider the problem for nonlinear elastic body with damping coefficient; existence and uniqueness of the solution for the steady state problem is proven. The stability of the dynamical nonlinear plate problem under certain conditions on the applied loads is investigated. Second, we explore the fluid structure interaction problem with Darcy flow in porous media. Energy functional for the displacement field of the plate and the gradient pressure of the fluid flow is built in an appropriate Sobolev type norm. We show that for a class of boundary conditions the energy functional is limited by the flux of mass through the inlet boundary.

10 
Optimal control for stochastic heat equation with memory
Volume 3, Number 1, Pages: 35  58, 2014
Fulvia Confortola
and Elisa Mastrogiacomo
Abstract
References
Full Text
Related Articles
In this paper, we investigate the existence and uniqueness of solutions for a class
of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal
control problem when the control enters the system together with the noise.

Go to top

