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MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.
MCRF is a quarterly publication in March, June, September and December. The journal will be online only. It is edited by a group of international leading experts in mathematical control theory and related fields. A key feature of MCRF is the journal's rapid publication, with a special emphasis on the highest scientific standard. The journal is essential reading for scientists and researchers who wish to keep abreast of the latest developments in the field. MCRF is a publication of the American Institute of Mathematical Sciences. All rights reserved.
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TOP 10 Most Read Articles in MCRF, March 2017
1 
A deterministic linear quadratic timeinconsistent
optimal control problem
Volume 1, Number 1, Pages: 83  118, 2011
Jiongmin Yong
Abstract
References
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A timeinconsistent optimal control problem is formulated and
studied for a controlled linear ordinary differential equation with
a quadratic cost functional. A notion of timeconsistent equilibrium
strategy is introduced for the original timeinconsistent problem.
Under certain conditions, we construct an equilibrium strategy which
can be represented via a RiccatiVolterra integral equation system.
Our approach is based on a study of multiperson hierarchical
differential games.

2 
Numerical methods for dividend optimization using
regimeswitching jumpdiffusion models
Volume 1, Number 1, Pages: 21  40, 2011
Zhuo Jin,
George Yin
and Hailiang Yang
Abstract
References
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This work develops numerical methods for finding optimal dividend
policies to maximize the expected present value of dividend
payout, where the surplus follows a regimeswitching jump
diffusion model and the switching is represented by a
continuoustime Markov chain. To approximate the optimal dividend
policies or optimal controls, we use Markov chain approximation
techniques to construct a discretetime controlled Markov chain
with two components. Under simple conditions, we prove the
convergence of the approximation sequence to the surplus process
and the convergence of the approximation to the value function.
Several examples are provided to demonstrate the performance of
the algorithms.

3 
Global wellposedness and asymptotic behavior of a class of initialboundaryvalue problem of the
KortewegDe Vries equation on a finite domain
Volume 1, Number 1, Pages: 61  81, 2011
Ivonne Rivas,
Muhammad Usman
and BingYu Zhang
Abstract
References
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In this paper, we study a class of initial boundary value problem
(IBVP) of the Kortewegde Vries equation posed on a finite interval
with nonhomogeneous boundary conditions. The IBVP is known to be
locally wellposed, but its global $L^2$ a priori estimate
is not available and therefore it is not clear whether its solutions
exist globally or blow up in finite time. It is shown in this paper
that the solutions exist globally as long as their initial value and
the associated boundary data are small, and moreover, those
solutions decay exponentially if their boundary data decay
exponentially.

4 
On the fast solution of evolution equations with a rapidly decaying source term
Volume 1, Number 1, Pages: 1  20, 2011
Alain Haraux
Abstract
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If $L$ is the generator of a uniformly bounded group of operators $T(t)$ on a Banach space $X$, the abstract evolution
equation $ u' + Lu(t) = h(t) $ has a (weak) solution tending to $0$ as
$t\rightarrow +\infty $ if, and only if $\int_0^{+\infty}T(s) h(s) ds $ is semiconvergent, and then this solution is unique.
For the semilinear equation $ u' + Lu(t) + f(u) = h(t) $, if $f$ such that $f(0) = 0$ is Lipschitz continuous on bounded subsets
of $X$ and has a Lipschitz constant bounded by
$ Cr^\alpha $ in the ball $B(0, r)$ for $r\leq r_0$, for any $h$ satisfiying
$h(t) \leq c(1+t)^{(1+ \lambda )} $
with $\lambda >\frac{1}{\alpha}$ and $c$ small enough
there exists a unique solution tending to $0$ at least like $(1+t)^{ \lambda}.$ When the system is dissipative,
this special solution makes it sometimes possible to estimate from below the rate of decay to $0$ of the other solutions.

5 
Cesaritype conditions for semilinear elliptic equation with leading term containing controls
Volume 1, Number 1, Pages: 41  59, 2011
Bo Li
and Hongwei Lou
Abstract
References
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An optimal control problem governed by semilinear elliptic partial
differential equation is considered. The equation is in divergence
form with the leading term containing controls. By studying the
$G$closure of the leading term, an existence result is established
under a Cesaritype condition.

6 
Rate of $L^2$concentration of the blowup solution
for critical nonlinear Schrödinger equation with potential
Volume 1, Number 1, Pages: 119  127, 2011
Jian Zhang,
Shihui Zhu
and Xiaoguang Li
Abstract
References
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We consider the blowup solutions of the Cauchy problem for the
critical nonlinear Schrödinger equation with a repulsive
harmonic potential. In terms of Merle and Tsutsumi's arguments as
well as Carles' transform, the $L^2$concentration property of
radially symmetric blowup solutions is obtained.

7 
Control of a network of magnetic ellipsoidal samples
Volume 1, Number 2, Pages: 129  147, 2011
Shruti Agarwal,
Gilles Carbou,
Stéphane Labbé
and Christophe Prieur
Abstract
References
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In this work, we present a mathematical study of stability and
controllability of onedimensional network of ferromagnetic
particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particles is described by the LandauLifschitz equation. First, we model a network of ellipsoidal shape
ferromagnetic particles. Then, we prove the stability of relevant
configurations and discuss the controllability by the means of the
external magnetic field induced by the magnetic dipole.
Finally some
numerical results illustrate the stability and the controllability results.

8 
Global Carleman inequalities for Stokes and penalized Stokes equations
Volume 1, Number 2, Pages: 149  175, 2011
Mehdi Badra
Abstract
References
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In this note we use the result of [22] to prove a global Carleman inequality related to the null controllability of penalized Stokes kind systems. The constants of the obtained Carleman inequality are uniform in terms of the penalization parameter $\varepsilon$. It then provides a null control with a uniformly (in $\varepsilon$) bounded $L^2$ norm. With a limiting argument we also deduce a new Carleman inequality for Stokes type system. Thus, we apply theses results to obtain the null controllability of Oseen and NavierStokes system in the penalized and in the non penalized cases.

9 
Observability of heat processes by transmutation without geometric restrictions
Volume 1, Number 2, Pages: 177  187, 2011
Sylvain Ervedoza
and Enrique Zuazua
Abstract
References
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The goal of this note is to explain how transmutation techniques (originally introduced in [14] in the context of the control of the heat equation, inspired on the classical Kannai transform, and recently revisited in [4] and adapted to deal with observability problems) can be applied to derive observability results for the heat equation without any geometric restriction on the subset in which the control is being applied, from a good understanding of the wave equation. Our arguments are based on the recent results in [15] on the frequency depending observability inequalities for waves without geometric restrictions, an iteration argument recently developed in [13] and the new representation formulas in [4] allowing to make a link between heat and wave trajectories.

10 
Exact controllability of a multilayer RaoNakra plate with free boundary conditions
Volume 1, Number 2, Pages: 189  230, 2011
Scott W. Hansen
and Oleg Yu Imanuvilov
Abstract
References
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Exact controllability of a multilayer plate system
with free boundary conditions are
obtained by the method of Carleman estimates. The multilayer plate system
is a natural multilayer generalization of a threelayer "sandwich
plate'' system due to Rao and Nakra. In the multilayer version, $m$
shear deformable layers alternate with $m+1$ layers modeled under
Kirchoff plate assumptions. The resulting system involves $m+1$
Lamé systems coupled with a scalar Kirchhoff plate equation. The
controls are taken to be distributed in a neighborhood of the boundary.
This paper is the sequel to [2] in which only clamped and hinged boundary conditions are considered.

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