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

Alberto Bressan; Massimo Fonte

doi:10.3934/dcds.2005.13.1

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2005, Volume 13, Issue 1: 1-12. Doi: 10.3934/dcds.2005.13.1

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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

Received: February 29, 2004

Revised: October 31, 2004

Published: March 2005

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q20, 76P05, 82A40, 35B40.

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