## Journals

- Advances in Mathematics of Communications
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- 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
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- Mathematical Foundations of Computing
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- AIMS Mathematics
- Conference Publications
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- Mathematics in Engineering

### Open Access Journals

DCDS-B

In this paper, we consider the following quasilinear attraction-repulsion chemotaxis system of parabolic-parabolic type
\begin{equation*}
\left\{
\begin{split}
&u_t=\nabla\cdot(D(u)\nabla u)-\nabla\cdot(\chi u\nabla v)+\nabla\cdot(\xi u\nabla w),\qquad & x\in\Omega,\,\, t>0,\\
&v_t=\Delta v+\alpha u-\beta v,\qquad &x\in\Omega, \,\,t>0,\\
&w_t=\Delta w+\gamma u-\delta w,\qquad &x\in\Omega,\,\, t>0
\end{split}
\right.
\end{equation*}
under homogeneous Neumann boundary conditions, where $D(u)\geq c_D (u+\varepsilon)^{m-1}$ and $\Omega\subset\mathbb{R}^2$ is a bounded domain with smooth boundary. It is shown that whenever $m>1$, for any sufficiently smooth nonnegative initial data, the system admits a global bounded classical solution for the case of non-degenerate diffusion (i.e., $\varepsilon>0$), while the system possesses a global bounded weak solution for the case of degenerate diffusion (i.e., $\varepsilon=0$).

CPAA

In this paper, we consider a reaction-diffusion system coupled by
nonlinear memory. Under appropriate hypotheses, we prove that the
solution either exists globally or blows up in finite time.
Furthermore, the blow-up rate estimates are obtained.

CPAA

This paper deals with the blow-up properties of solutions to a
degenerate parabolic system coupled via nonlinear boundary flux.
Firstly, we construct the self-similar supersolution and
subsolution to obtain the critical global existence curve.
Secondly, we establish the precise blow-up rate estimates for solutions which blow up
in a finite time. Finally, we investigate the localization of blow-up points. The critical
curve of Fujita type is conjectured with the aid of some new results.

DCDS-S

Traffic congestion visualization is an important part in traffic information service. However, the real-time data is difficult to obtain and its analysis method is not accurate, so the reliability of congestion state visualization is low. This paper proposes a visualization analysis algorithm of traffic congestion based on Floating Car Data (FCD), which utilizes the FCD to estimate and display dynamic traffic state on the electronic map. Firstly, an improved map matching method is put forward to match rapidly the FCD with road sections, which includes two steps of coarse and precise matching. Then, the traffic speed is estimated and classified to display different traffic states. Eventually, multi-group experiments have been conducted based on more than 8000 taxies in Xi’an. The experimental results show that FCD can be matched accurately with the selected road sections which accuracy can reach up to \({\rm{96\% }}\), and the estimated traffic real-time state can achieve \({\rm{94\% }}\) in terms of reliability. So this visualization analysis algorithm can display accurately road traffic state in real time.

MCRF

In this paper we study controllability and stabilizability of a
class of distributed parameter control system described by the
Kawahara equation posed on a periodic domain $\mathbb{T}$ with
internal control acting on a sub-domain $\omega $ of $\mathbb{T}$.
Earlier in [42], aided by Bourgain smoothing property of
the system, we showed that the system is locally exactly
controllable and exponentially stabilizable. In this paper, helped
further by certain properties of propagation of compactness and
regularity in Bourgain spaces for the solutions of the associated
linear system, we show that the system is globally exactly
controllable and globally exponentially stabilizable.

CPAA

In this paper, we study the existence of local/global solutions to the Cauchy problem
\begin{eqnarray}
\rho(x)u_t=\Delta u+q(x)u^p, (x,t)\in R^N \times (0,T),\\
u(x,0)=u_{0}(x)\ge 0, x \in R^N
\end{eqnarray}
with $p > 0$ and $N\ge 3$. We describe the sharp decay conditions on $\rho, q$ and the data $u_0$ at infinity that guarantee the local/global existence of nonnegative solutions.

keywords:
global existence
,
Fujita exponent
,
Cauchy problem
,
inhomogeneous heat equation.
,
Local existence

DCDS

In this paper, we investigate the quasilinear Keller-Segel equations (q-K-S):
\[
\left\{
\begin{split}
&n_t=\nabla\cdot\big(D(n)\nabla n\big)-\nabla\cdot\big(\chi(n)\nabla c\big)+\mathcal{R}(n), \qquad x\in\Omega,\,t>0,\\
&\varrho c_t=\Delta c-c+n, \qquad x\in\Omega,\,t>0,
\end{split}
\right.
\]
under homogeneous Neumann boundary conditions in a bounded domain $\Omega\subset\mathbb{R}^N$. For both $\varrho=0$ (parabolic-elliptic case) and $\varrho>0$ (parabolic-parabolic case), we will show the global-in-time existence and uniform-in-time boundedness of solutions to equations (q-K-S) with both non-degenerate and

*degenerate*diffusions on the*non-convex*domain $\Omega$, which provide a supplement to the dichotomy boundedness vs. blow-up in parabolic-elliptic/parabolic-parabolic chemotaxis equations with degenerate diffusion, nonlinear sensitivity and logistic source. In particular, we improve the recent results obtained by Wang-Li-Mu (2014, Disc. Cont. Dyn. Syst.) and Wang-Mu-Zheng (2014, J. Differential Equations).
CPAA

This paper deals with the blow-up properties and asymptotic
behavior of solutions to a semilinear integrodifferential system
with nonlocal reaction terms in space and time. The blow-up
conditions are given by a variant of the eigenfunction method
combined with new properties on systems of differential
inequalities. At the same time, the blow-up set is obtained. For
some special cases, the asymptotic behavior of the blow-up
solution is precisely characterized.

BDIA

Urban air pollution post a great threat to human health, and has been a major concern of many metropolises in developing countries. Lately, a few air quality monitoring stations have been established to inform public the real-time air quality indices based on fine particle matters, e.g. $PM_{2.5}$, in countries suffering from air pollutions. Air quality, unfortunately, is fairly difficult to manage due to multiple complex human activities from driving to smelting. We observe that human activities' hidden regular pattern offers possibility in predication, and this motivates us to infer urban air condition from the perspective of time series. In this paper, we focus on $PM_{2.5}$ based urban air quality, and introduce two kinds of time-series methods for real-time and fine-grained air quality prediction, harnessing historical air quality data reported by existing monitoring stations. The methods are evaluated based in the real-life $PM_{2.5}$ concentration data in the year of 2013 (January - December) in Wuhan, China.

## Year of publication

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