We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. Thi...We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.展开更多
In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on tw...In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries （KdV） equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coe^cient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10921101)the Programme of Introducing Talents of Discipline to Universities of China(Grant No.B12023)the Fundamental Research Funds of Shandong University
文摘We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables （t, x） ∈[0, T]× R^d. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman- Kac formula for a general non-Markoviau BSDE. Some main properties of solutions of this new PDEs are also obtained.
基金Supported by the Key Project of Chinese Ministry of Education under Grant No.211123the Scientific Research Fund of Hunan Provincial Education Department under Grant No.10B072+1 种基金Doctor Scientific Research Startup Project Foundation of Hunan University of Arts and Science under Grant No.BSQD1010the Fund of Key Construction Academic Subject of Hunan Province
文摘In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries （KdV） equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coe^cient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.
