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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.
The journal adheres to the publication ethics and malpractice policies outlined by COPE.

TOP 10 Most Read Articles in EECT, April 2014
1 
Preface
Volume 1, Number 1, Pages: i  i, 2012
Alain Haraux
and Irena Lasiecka
Abstract
Full Text
Related Articles
The present Inaugural Volume is the first Issue of a new journal
Evolution Equations and Control Theory [EECT], which is published within the AIMS Series. EECT is devoted to topics
lying at the interface between Evolution Equations and Control Theory of Dynamics.
Evolution equations are to be understood in a broad sense as Infinite Dimensional Dynamics which often arise in
modeling physical systems as an infinitedimensional process. This includes single PDE (Partial Differential Equations) or FDE (Functional Differential Equations) as well as coupled dynamics of different characteristics with an interface between them.
Since modern control theory intrinsically depends on a good understanding of the qualitative theory of dynamics
and evolution theory, the choice of these two topics appears synergistic and most natural.
Past experience shows that new developments in control theory often depend on
sufficient information related to the associated dynamical properties of the system. On the other hand,
developments in evolution theory allow one to consider certain control theoretic
formulations that alone would not appear treatable.
For more information please click the "Full Text" above.

2 
Internal stabilization of NavierStokes equation with exact controllability on spaces with finite codimension
Volume 1, Number 1, Pages: 1  16, 2012
Viorel Barbu
and Ionuţ Munteanu
Abstract
References
Full Text
Related Articles
One designs an internal stabilizing feedback controller, for the NavierStokes equations, which steers, in finite time, the initial value $X_o$ in $X_e+\mathcal{X}_s$, where $X_e$ is any equilibrium solution and $\mathcal{X}_s$ is a finite codimensional space, consisting of stable modes.

3 
On KelvinVoigt model and its generalizations
Volume 1, Number 1, Pages: 17  42, 2012
Miroslav Bulíček,
Josef Málek
and K. R. Rajagopal
Abstract
References
Full Text
Related Articles
We consider a generalization of the KelvinVoigt model where
the elastic part of the Cauchy stress depends nonlinearly on
the linearized strain and the dissipative part of the Cauchy
stress is a nonlinear function of the symmetric part of the
velocity gradient. The assumption that the Cauchy stress
depends nonlinearly on the linearized strain can be justified
if one starts with the assumption that the kinematical
quantity, the left CauchyGreen stretch tensor, is a nonlinear
function of the Cauchy stress, and linearizes under the
assumption that the displacement gradient is small. Longtime
and large data existence, uniqueness and regularity properties
of weak solution to such a generalized KelvinVoigt model are
established for the nonhomogeneous mixed boundary value
problem. The main novelty with regard to the mathematical analysis consists
in including nonlinear (nonquadratic) dissipation in the problem.

4 
Invariance for stochastic reactiondiffusion equations
Volume 1, Number 1, Pages: 43  56, 2012
Piermarco Cannarsa
and Giuseppe Da Prato
Abstract
References
Full Text
Related Articles
Given a stochastic reactiondiffusion equation on a bounded open subset $\mathcal O$ of $\mathbb{R}^n$, we discuss conditions for the invariance of a nonempty closed convex subset $K$ of $L^2(\mathcal O)$ under the corresponding flow.
We obtain two general results under the assumption that the fourth power of the distance from $K$ is of class $C^2$,
providing, respectively, a necessary and a sufficient condition for invariance. We also study the example where $K$ is the cone of all nonnegative functions in $L^2(\mathcal O)$.

5 
Semiweak wellposedness and attractors for
2D SchrödingerBoussinesq equations
Volume 1, Number 1, Pages: 57  80, 2012
Igor Chueshov
and Alexey Shcherbina
Abstract
References
Full Text
Related Articles
We deal with an initial boundary value problem for the
SchrödingerBoussinesq system
arising in plasma physics in twodimensional domains.
We prove the global Hadamard wellposedness of this problem
(with respect to the topology which is weaker than topology associated
with the standard variational (weak) solutions)
and study properties of
the solutions. In the dissipative case the existence of a global attractor
is established.

6 
Optimal control of advective direction in
reactiondiffusion population models
Volume 1, Number 1, Pages: 81  107, 2012
Heather Finotti,
Suzanne Lenhart
and Tuoc Van Phan
Abstract
References
Full Text
Related Articles
We investigate optimal control of the advective coefficient in a class of
parabolic partial differential equations, modeling a population with
nonlinear growth. This work is motivated by the question: Does movement toward
a better resource environment benefit a population?
Our objective functional is formulated with interpreting "benefit"
as the total population size integrated over our finite time interval.
Results on existence, uniqueness, and characterization of the optimal
control are established. Our numerical illustrations for several growth functions and resource
functions indicate that movement along the resource spatial gradient benefits the population, meaning
that the optimal control is close to the spatial gradient of the
resource function.

7 
Certain questions of feedback stabilization for NavierStokes equations
Volume 1, Number 1, Pages: 109  140, 2012
Andrei Fursikov
and Alexey V. Gorshkov
Abstract
References
Full Text
Related Articles
The authors study the stabilization problem for NavierStokes and
Oseen equations near steadystate solution by feedback control.
The cases of control in initial condition (start control) as well
as impulse and distributed controls in right side supported in a
fixed subdomain of the domain $G$ filled with a fluid are
investigated. The cases of bounded and unbounded domain $G$ are
considered.

8 
Carleman estimates for some anisotropic
elasticity systems and applications
Volume 1, Number 1, Pages: 141  154, 2012
Victor Isakov
Abstract
References
Full Text
Related Articles
We show that under some conditions one can obtain Carleman type estimates for the transversely isotropic elasticity system with residual stress. We consider both time dependent and static cases.
The main idea is to reduce this system to a principally upper triangular one and the main technical tool is Carleman estimates with two large parameters for general second order partial differential operators.

9 
Modeling of a nonlinear plate
Volume 1, Number 1, Pages: 155  169, 2012
Shun Li
and PengFei Yao
Abstract
References
Full Text
Related Articles
We consider modeling of a nonlinear thin plate
under the following assumptions: (a) the materials are nonlinear;
(b) the deflections are small (linear strain displacement
relations). When the middle surface is planar, we consider the
bending of a plate to establish the strain energy, the equilibrium
equations, and the motion equations. For a shell with a curved
middle surface in $\mathbb{R}^3$, we derive a nonlinear model where a
deformation in threedimensions is concerned.

10 
On wellposedness of incompressible twophase flows with phase transitions: The case of equal densities
Volume 1, Number 1, Pages: 171  194, 2012
Jan Prüss,
Yoshihiro Shibata,
Senjo Shimizu
and Gieri Simonett
Abstract
References
Full Text
Related Articles
The basic model for incompressible twophase flows with phase transitions is derived from basic principles and shown to be thermodynamically consistent in the sense that the total energy is conserved and the total entropy is nondecreasing. The local wellposedness of such problems is proved by means of the technique of
maximal $L_p$regularity in the case of equal densities. This way we obtain a local semiflow on a welldefined nonlinear state manifold. The equilibria of the system in absence of external forces are identified and it is shown that the negative total entropy is a strict Ljapunov functional for the system. If a solution does not develop singularities, it is proved that it exists globally in time, its orbit is relatively compact, and its limit set is nonempty and contained in the set of equilibria.

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