## 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
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS-B

One particular metric that generates the weak topology on the weak global attractor $\mathcal{A}_w$ of three dimensional incompressible Navier-Stokes equations is introduced and used to obtain an upper bound for the Kolmogorov entropy of $\mathcal{A}_w$. This bound is expressed explicitly in terms of the physical parameters of the fluid flow.

DCDS

We study linearly degenerate hyperbolic systems
of rich type in one space dimension. It is showed that such a system admits exact
traveling wave solutions after a finite time, provided that the initial data are
Riemann type outside a space interval. We prove the convergence of entropy
solutions toward traveling waves in the $L^1$ norm as the time goes to infinity.
The traveling waves are determined explicitly in terms of the initial data and
the system. We also obtain the stability of entropy solutions in $L^1$. Applications
concern physical models such as the generalized extremal surface equations, the
Born-Infeld system and augmented Born-Infeld system.

keywords:
Entropy solution
,
long-time behavior
,
rich system
,
$L^1$ stability.
,
linearly degeneracy

JIMO

In this paper, we present a new global optimization method to solve
nonlinear systems of equations. We reformulate given system of
nonlinear equations as a global optimization problem and then give a
new auxiliary function method to solve the reformulated global
optimization problem. The new auxiliary function proposed in this
paper can be a filled function, a quasi-filled function or a strict
filled function with appropriately chosen parameters. Several
numerical examples are presented to illustrate the efficiency of the
present approach.

JIMO

A filled function method is presented in this paper to solve
constrained nonlinear integer programming problems. It is shown that
for a given non-global local minimizer, a better local minimizer can
be obtained by local search staring from an improved initial point
which is obtained by locally solving a box-constrained integer
programming problem. Several illustrative numerical examples are
reported to show the efficiency of the present method.

JIMO

In this paper, we study a new exact and smooth penalty function for
semi-infinite programming problems with continuous inequality
constraints. Through this exact penalty function, we can transform a
semi-infinite programming problem into an unconstrained optimization
problem. We find that, under some reasonable conditions when the
penalty parameter is sufficiently large, the local minimizer of this
penalty function is the local minimizer of the primal problem.
Moreover, under some mild assumptions, the local exactness property
is explored. The numerical results demonstrate that it is an
effective and promising approach for solving constrained
semi-infinite programming problems.

CPAA

For inhomogeneous diagonal system with distinct characteristics or
with characteristics with constant multiplicity, under the
assumption that the system is linearly degenerate and the $C^1$ norm
of the initial data is bounded, we show that the mechanism of the
formation of singularities of classical solution to its Cauchy
problem must be of ODE type. Similar results are also obtained for
corresponding mixed initial-boundary value problems on a
semi-unbounded domain.

## Year of publication

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