In this article, we investigate a class of stochastic neutral partial functional differential equations. By establishing new integral inequalities, the attracting and quasi-invariant sets of stochastic neutral partial functional differential equations are obtained. The results in [15, 16] are generalized and improved.
With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver's random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations.
Associated to every symmetrizable generalized intersection matrix A, we define a Lie algebra, called an SIM-Lie algebra. We prove that SIM-Lie algebras keep unchange under braid-equivalences. Two special cases are considered. In the case when A is a symmetrizable generalized Cartan matrix, we show that the corresponding SIM-Lie algebra is just the Kac-Moody Lie algebra. In another case when A is an intersection matrix, we prove that the corresponding SIM-Lie algebra is just the intersection matrix Lie algebra in the sense of Slodowy.
mapping of finite distortion;weighted Grotzsch problem;weighted Nitsche problem
This note deals with the existence and uniqueness of a minimiser of the following Grotzsch-type problem under some mild conditions, where F denotes the set of all homeomorphims f with finite linear distortion K(z, f) between two rectangles Q_1 and Q_2 taking vertices into vertices, φ is a positive, increasing and convex function, and λ is a positive weight function. A similar problem of Nitsche-type, which concerns the minimiser of some weighted functional for mappings between two annuli, is also discussed. As by-products, our discussion gives a unified approach to some known results in the literature concerning the weighted Grotzsch and Nitsche problems.
[Xia, Anyin] Xihua Univ, Sch Sci, Chengdu 610039, Sichuan, Peoples R China.;[Xia, Anyin] Sichuan Univ, Dept Math, Chengdu 610065, Sichuan, Peoples R China.;[Fan, Mingshu] Southwest Jiaotong Univ, Dept Math, Chengdu 610031, Sichuan, Peoples R China.;[Li, Shan] Sichuan Univ, Business Sch, Chengdu 610065, Sichuan, Peoples R China.
[Li, Shan] Sichuan Univ, Business Sch, Chengdu 610065, Sichuan, Peoples R China.
porous medium systems;Dirichlet boundary conditions;global existence;blow-up;upper and lower bounds
This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs.
[张文晰] Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu 610039, China;[薛锋] School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610031, China;[陈崇双] Department of Statistics, School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China;[牟峰; 张文晰] School of Transportation and Automotive Engineering, Xihua University, Chengdu 610039, China