%0 Journal Article
%J Discrete Contin. Dyn. Syst. 13 (2005) 1-12
%D 2005
%T On the Blow-up for a Discrete Boltzmann Equation in the Plane
%A Alberto Bressan
%A Massimo Fonte
%X We 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.
%B Discrete Contin. Dyn. Syst. 13 (2005) 1-12
%G en_US
%U http://hdl.handle.net/1963/2244
%1 2000
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-17T09:31:05Z\\nNo. of bitstreams: 1\\n0403047v2.pdf: 116770 bytes, checksum: a7432c5b660f4e4672c952003dd0210f (MD5)
%0 Report
%D 2005
%T An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation
%A Alberto Bressan
%A Massimo Fonte
%X In 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.
%B Methods Appl. Anal. 12 (2005) 191-219
%G en_US
%U http://hdl.handle.net/1963/1719
%1 2432
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-01-24T09:03:54Z\\nNo. of bitstreams: 1\\nmath.AP0504450.pdf: 261370 bytes, checksum: 75945d031343a82836b46ab9705ed6de (MD5)