00648nas a2200109   4500008004300000245006600043210005800109520029500167100002100462700001900483856003600502       2005                        en_Ud  00aOn the Blow-up for a Discrete Boltzmann Equation in the Plane0 aBlowup for a Discrete Boltzmann Equation in the Plane3 aWe study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final section, a possible blow-up scenario is discussed.1 aBressan, Alberto1 aFonte, Massimo  uhttp://hdl.handle.net/1963/224400982nas a2200109   4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836       2005                        en_Ud  00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.1 aBressan, Alberto1 aFonte, Massimo  uhttp://hdl.handle.net/1963/1719