## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
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- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
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- AIMS Mathematics

DCDS

In this paper, we study an optimal control problem for
semilinear evolution equations with a mixed constraint of the state and the
control. One of the motivations is the problem with a state dependent control
domain. Our main result is the Pontryagin type necessary conditions for the
optimal controls. The main tools we use are the Ekeland variational principle
and the spike perturbation technique.

JIMO

Some widely used short interest rate term
structure models are discussed. By establishing certain estimates
on the solutions of stochastic differential inequalities, we found
that the interest rate processes obtained from these models do not
have enough integrability which leads to some defects in several
applications.

DCDS-B

Professor David L. Russell just celebrated his 70th
birthday in 2009. His numerous important and fundamental
contributions to the control theory of partial differential
equations have won him recognitions as a true pioneer and giant in
this field. And his pleasant personality and ready helpfulness have
won our hearts as his admirers, students, and friends.

Prof. Russell's lifetime love and interests are control theory and partial differential equations. We have asked Goong Chen, a former PhD student of Prof. Russell, to write a survey of his career and mathematical work. Moreover, as a way to pay our tribute to him, it is only proper here that we put together a collection of papers by researchers who work on these and closely related subjects of Prof. Russell's. Indeed, the topics collected are extensive, including the theory and applications of analysis, computation, control, optimization, etc., for various systems arising from conservation laws and quasilinear hyperbolic systems, fluids, mathematical finance, neural networks, reaction-diffusion, structural dynamics, stochastic PDEs, thermoelasticity, viscoelasticity, etc. They are covered in great depth by the authors. There are a total of 35 papers finally accepted for publication after going through strict manuscript reviews and revision. Due to the large number of papers on hand, we divide them into Groups I (20 papers) and II (15 papers). Papers in Group I are published in Discrete and Continuous Dynamical Systems-Series B (DCDS-B) Volume 14, No. 4 (2010), while those in Group II are published in Journal of Systems Science and Complexity (JSSC) Volume 23, No. 3 (2010). This division is up to the preference of the authors. We thank all the authors and reviewers for their critical contributions and valuable assistance that make the publication of these two journal issues possible.

For more information please click the “Full Text” above.

Prof. Russell's lifetime love and interests are control theory and partial differential equations. We have asked Goong Chen, a former PhD student of Prof. Russell, to write a survey of his career and mathematical work. Moreover, as a way to pay our tribute to him, it is only proper here that we put together a collection of papers by researchers who work on these and closely related subjects of Prof. Russell's. Indeed, the topics collected are extensive, including the theory and applications of analysis, computation, control, optimization, etc., for various systems arising from conservation laws and quasilinear hyperbolic systems, fluids, mathematical finance, neural networks, reaction-diffusion, structural dynamics, stochastic PDEs, thermoelasticity, viscoelasticity, etc. They are covered in great depth by the authors. There are a total of 35 papers finally accepted for publication after going through strict manuscript reviews and revision. Due to the large number of papers on hand, we divide them into Groups I (20 papers) and II (15 papers). Papers in Group I are published in Discrete and Continuous Dynamical Systems-Series B (DCDS-B) Volume 14, No. 4 (2010), while those in Group II are published in Journal of Systems Science and Complexity (JSSC) Volume 23, No. 3 (2010). This division is up to the preference of the authors. We thank all the authors and reviewers for their critical contributions and valuable assistance that make the publication of these two journal issues possible.

For more information please click the “Full Text” above.

keywords:

MCRF

Professor Xunjing Li was born in Qingdao, Shandong Province, China,
on the 13th June 1935. Shandong is a province with a rich culture
that has nurtured a great number of influential intellectuals during
its long history, including Confucius. Immediately after his
graduation from the Department of Mathematics at Shandong University
in 1956, Professor Li was enrolled into the master program at Fudan
University specializing in function approximation theory, supervised
by Professor Jiangong Chen, one of the most prominent Chinese
mathematicians in modern history. He stayed at Fudan as an Assistant
Lecturer upon graduation in 1959, and was promoted to Lecturer,
Associate Professor and Professor in 1962, 1980, and 1984,
respectively. He became a Chair Professor in 1997, before retiring
in 2001. He died of cancer in February 2003 at the age of 68.

For more information please click the “Full Text” above

For more information please click the “Full Text” above

keywords:

JIMO

An open-loop two-person zero-sum linear quadratic (LQ for short)
stochastic differential game is considered. The controls for both
players are allowed to appear in both the drift and diffusion of the
state equation, the weighting matrices in the payoff/cost functional
are not assumed to be definite/non-singular, and the cross-terms
between two controls are allowed to appear. A forward-backward
stochastic differential equation (FBSDE, for short) and a
generalized differential Riccati equation are introduced, whose
solvability leads to the existence of the open-loop saddle points
for the corresponding two-person zero-sum LQ stochastic differential
game, under some additional mild conditions. The main idea is a
thorough study of general two-person zero-sum LQ games in Hilbert
spaces.

keywords:
Hilbert method.
,
open-loop controls
,
Stochastic games
,
linear-quadratic
,
saddle points

MCRF

A time-inconsistent optimal control problem is formulated and
studied for a controlled linear ordinary differential equation with
a quadratic cost functional. A notion of time-consistent equilibrium
strategy is introduced for the original time-inconsistent problem.
Under certain conditions, we construct an equilibrium strategy which
can be represented via a Riccati--Volterra integral equation system.
Our approach is based on a study of multi-person hierarchical
differential games.

MCRF

A general time-inconsistent optimal control problem is considered
for stochastic differential equations with deterministic
coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman
type equation is derived for the equilibrium value function of the
problem. Well-posedness such an equation is studied, and
time-consistent equilibrium strategies are constructed. As special
cases, the linear-quadratic problem and a generalized Merton's
portfolio problem are investigated.

MCRF

An optimal control problem for a semilinear elliptic equation of divergenceform is considered. Both the leading term and the semilinear term of the state equationcontain the control. The well-known Pontryagin type maximum principle for the optimal controls is the *first*-order necessary condition. When such a first-order necessary condition is singular in some sense, certain type of the *second*-order necessary condition will come in naturally. The aim of this paper is to explore such kind of conditions for our optimal control problem.

MCRF

A linear-quadratic (LQ, for short) optimal control problem is considered
for mean-field stochastic differential equations with constant
coefficients in an infinite horizon. The stabilizability of the
control system is studied followed by the discussion of the
well-posedness of the LQ problem. The optimal control can be
expressed as a linear state feedback involving the state and its
mean, through the solutions of two algebraic Riccati equations. The
solvability of such kind of Riccati equations is investigated by
means of semi-definite programming method.

MCRF

Optimal control problems of forward-backward stochastic Volterra
integral equations (FBSVIEs, in short) are formulated and studied. A
general duality principle is established for linear backward
stochastic integral equation and linear stochastic Fredholm-Volterra
integral equation with mean-field. With the help of such a duality
principle, together with some other new delicate and subtle skills,
Pontryagin type maximum principles are proved for two optimal
control problems of FBSVIEs.

## Year of publication

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