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- Wen Shen
- 1997

Consider a scalar O.D.E. of the form _ x = f (t; x), where f is possibly discontinuous w.r.t. both variables t; x. Under suitable assumptions , we prove that the corresponding Cauchy problem admits a unique solution, which depends HH older continuously on the initial data. Our result applies in particular to the case where f can be written in the form f (t;… (More)

- Alberto Bressan, Wen Shen
- Int. J. Game Theory
- 2004

The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls,… (More)

- Wen Shen, Zhengfu Xu
- 2006

We study high order convergence of vanishing viscosity approximation to scalar hyperbolic conservation laws in one space dimension. We prove that, under suitable assumptions, in the region where the solution is smooth, the viscous solution admits an expansion in powers of the viscosity parameter ε. This allows an extrapolation procedure that yields high… (More)

- Wen Shen, Vahan Babushkin, Zeyar Aung, Wei Lee Woon
- e-Energy
- 2013

In this work, we try to solve the problem of day-ahead prediction of electricity demand using an ensemble forecasting model. Based on the Pattern Sequence Similarity (PSF) algorithm, we implemented five forecasting models using different clustering techniques: K-means model (as in original PSF), Self-Organizing Map model, Hierarchical Clustering model,… (More)

- Guangjie Han, Jinfang Jiang, Wen Shen, Lei Shu, Joel J. P. C. Rodrigues
- IET Information Security
- 2013

- Alberto Bressan, Wen Shen
- SIAM J. Control and Optimization
- 2004

- Alberto Bressan, Wen Shen
- 2006

We study a class of optimization problems for solutions to a hyperbolic system of balance laws. The controller can affect the evolution of the system through the source terms, as well as the boundary conditions. Our main goal is to obtain necessary conditions in order that a piecewise regular solution, with finitely many shocks, be optimal. These necessary… (More)

- Debora Amadori, Wen Shen
- 2009

In this paper we analyze a set of equations proposed by Hadeler and Kuttler [20], describing the flow of granular matter in terms of the heights of a standing layer and of a moving layer. By a suitable change of variables, the system can be written as a 2 × 2 hy-perbolic system of balance laws, which we study in the one-dimensional case. The system is… (More)

The paper is concerned with Nash equilibrium solutions for the Lighthill-Whitham model of traffic flow, where each driver chooses his own departure time in order to minimize the sum of a departure cost and an arrival cost. Estimates are provided, on how much the Nash solution may change, depending on the cost functions and on the flux function of the… (More)

We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for which one can not adapt the standard theory of conservation laws. We construct approximate solutions with a fractional… (More)