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

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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

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

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