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Journal of Statistical Physics

, Volume 149, Issue 4, pp 629–642 | Cite as

A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time

  • Tertuliano Franco
  • Pablo Groisman
Article
  • 172 Downloads

Abstract

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a strong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation t u= xx u+f(u). If f(u)=u p , 1<p≤3, we also obtain a law of large numbers for the explosion time.

Keywords

Hydrodynamic limit Parabolic equations Blow-up 

Notes

Acknowledgements

We want to thank Pablo Ferrari, Milton Jara and Mariela Sued for fruitful discussions.

PG is partially supported by UBACyT 20020090100208, ANPCyT PICT No. 2008-0315 and CONICET PIP 2010-0142 and 2009-0613. TF acknowledges support from ANPCyT Argentina through a post-doctoral fellowship.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Universidade Federal da BahiaSalvadorBrazil
  2. 2.Departamento de Matemática, Fac. Cs. Exactas y NaturalesUBA and IMAS-CONICETBuenos AiresArgentina

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