A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
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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.
KeywordsHydrodynamic limit Parabolic equations Blow-up
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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