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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.
 Publishes 4 issues a year in March, June, September and December.
 Publishes online only.
 Indexed in Science Citation IndexExpanded, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Web of Science, MathSciNet and Zentralblatt MATH.
 The journal adheres to the publication ethics and malpractice policies outlined by COPE.
 Archived in Portico and CLOCKSS.
 EECT is a publication of the American Institute of Mathematical Sciences. All rights reserved.

TOP 10 Most Read Articles in EECT, June 2017
1 
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
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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.

2 
Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III
Volume 2, Number 2, Pages: 423  440, 2013
Belkacem SaidHouari
and Radouane Rahali
Abstract
References
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In this paper, we investigate the decay property of a Timoshenko system in thermoelasticity
of type III in the whole space where the heat conduction is given by the Green and Naghdi theory.
Surprisingly, we show that the coupling of the Timoshenko system with the heat conduction of Green and Naghdi's theory
slows down the decay of the solution. In fact we show that the $L^2$norm of the solution decays like $(1+t)^{1/8}$, while in the case of the coupling of the Timoshenko system with
the Fourier or Cattaneo heat conduction, the decay rate is of the form $(1+t)^{1/4}$ [25]. We point out that the decay rate of
$(1+t)^{1/8}$ has been obtained provided that the initial data are in $L^1( \mathbb{R})\cap H^s(\mathbb{R}), (s\geq 2)$. If the wave speeds of the first two equations are different, then the decay rate of the solution is of regularityloss type, that is in this case the previous decay rate can be obtained only under an additional regularity assumption on the initial data.
In addition, by
restricting the initial data to be in $H^{s}\left( \mathbb{R}\right)\cap
L^{1,\gamma }\left( \mathbb{R}\right) $ with $
\gamma \in \left[ 0,1\right] $, we can derive faster decay estimates with
the decay rate improvement by a factor of $t^{\gamma/4}$.

3 
Regular solutions of wave equations with supercritical sources and exponentialtologarithmic damping
Volume 2, Number 2, Pages: 255  279, 2013
Lorena Bociu,
Petronela Radu
and Daniel Toundykov
Abstract
References
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We study regular solutions to wave equations with supercritical source terms, e.g., of exponent $p>5$ in 3D. Such sources have been a major challenge in the investigation of finiteenergy ($H^1 \times L^2$) solutions to wave PDEs for many years. The wellposedness has been settled in part, but even the local existence, for instance, in 3 dimensions requires the relation $p\leq 6m/(m+1)$ between the exponents $p$ of the source and $m$ of the viscous damping.
We prove that smooth initial data ($H^2 \times H^1$) yields regular solutions that do not depend on the above correlation. Local existence is demonstrated for any source exponent $p\geq 1$ and any monotone damping including feedbacks growing exponentially or logarithmically at infinity, or with no damping at all. The result holds in dimensions 3 and 4, and with some restrictions on $p$ in dimensions $n\geq 5$.
Furthermore, if we assert the classical condition that the damping grows as fast as the source, then these regular solutions are global.

4 
On LandauLifshitz equations of noexchange energy models in ferromagnetics
Volume 2, Number 4, Pages: 599  620, 2013
Wei Deng
and Baisheng Yan
Abstract
References
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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.

5 
Avoiding degeneracy in the Westervelt equation by state constrained optimal control
Volume 2, Number 2, Pages: 281  300, 2013
Christian Clason
and Barbara Kaltenbacher
Abstract
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The Westervelt equation, which describes nonlinear acoustic wave propagation in high intensity ultrasound applications, exhibits potential degeneracy for large acoustic pressure values. While wellposedness results on this PDE have so far been based on smallness of the solution in a higher order spatial norm, nondegeneracy can be enforced explicitly by a pointwise state constraint in a minimization problem, thus allowing for pressures with large gradients and higherorder derivatives, as is required in the mentioned applications. Using regularity results on the linearized state equation, wellposedness and necessary optimality conditions for the PDE constrained optimization problem can be shown via a relaxation approach by Alibert and Raymond [2].

6 
Energy methods for Hartree type equations
with inversesquare potentials
Volume 2, Number 3, Pages: 531  542, 2013
Toshiyuki Suzuki
Abstract
References
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Nonlinear Schrödinger equations
with nonlocal nonlinearities described by integral operators
are considered.
This generalizes usual Hartree type equations (HE)$_{0}$.
We construct weak solutions to (HE)$_{a}$, $a\neq 0$,
even if the kernel is of nonconvolution type.
The advantage of our methods is the applicability
to the problem with strongly singular potential $ax^{2}$
as a term in the linear part and
with critical nonlinearity.

7 
Rational decay rates for a PDE heatstructure interaction: A
frequency domain approach
Volume 2, Number 2, Pages: 233  253, 2013
George Avalos
and Roberto Triggiani
Abstract
References
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In this paper, we consider a simplified version of a fluidstructure PDE
model
in fact, a heatstructure interaction PDEmodel. It is intended to be a first step toward a more realistic fluidstructure PDE model which has been of longstanding interest within the mathematical and biological sciences [33, p. 121], [17], [19]. This physically more sound and mathematically more challenging model will be treated in [13]. The simplified model replaces the linear dynamic Stokes equation with a linear $n$dimensional heat equation (heatstructure interaction). The entire dynamics manifests both hyperbolic and parabolic features. Our main result is as follows: Given smooth initial datai.e., data in the domain of the associated semigroup generatorthe corresponding solutions decay at the rate $o( t^{\frac{1}{2}}) $
(see Theorem 1.3 below). The basis of our proof is the recently derived resolvent criterion in [15]. In order to apply it, however, suitable PDEestimates need to be established for each component by also making critical use of the interface conditions. A companion paper [6] will sharpen Lemma 5.8 of the present work by use of a lengthy and technical microlocal argument as in [26,29,30,31], to obtain the optimal value $\alpha =1$; hence, the optimal decay rate $o(t^{1})$. See Remarks 1.2,1.3.

8 
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
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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.

9 
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
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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.

10 
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
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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.

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