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A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
Authors:Tertuliano Franco  Pablo Groisman
Affiliation:1. Universidade Federal da Bahia, Salvador, Brazil
2. Departamento de Matem??tica, Fac. Cs. Exactas y Naturales, UBA and IMAS-CONICET, Buenos Aires, Argentina
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:
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