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April  2005, 13(1): 1-12. doi: 10.3934/dcds.2005.13.1

On the blow-up for a discrete Boltzmann equation in the plane

Alberto Bressan 1, and  Massimo Fonte 1,

1. 

S.I.S.S.A., Via Beirut, 2-4, 34014 Trieste, Italy

Received  March 2004 Revised  November 2004 Published  March 2005

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.
Keywords: Discrete Boltzmann equation, asymptotic behaviour and blow-up, Broadwell model..
Mathematics Subject Classification: Primary: 35Q20, 76P05, 82A40, 35B4.
Citation: Alberto Bressan, Massimo Fonte. On the blow-up for a discrete Boltzmann equation in the plane. Discrete & Continuous Dynamical Systems, 2005, 13 (1) : 1-12. doi: 10.3934/dcds.2005.13.1
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