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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)
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)
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)
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)