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19 April 2024

» arxiv » 1207.1574

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A particle system with explosions: law of large numbers for the density of particles and the blow-up time
Tertuliano Franco ; Pablo Groisman ;
Date:	6 Jul 2012
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 stong 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 u_t =u_{xx} + f(u). If f(u)=u^p, 1<p le 3, we also obtain a law of large numbers for the explosion time.
Source:	arXiv, 1207.1574
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