A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
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...
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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v149_n4_p629_Franco http://hdl.handle.net/20.500.12110/paper_00224715_v149_n4_p629_Franco |
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| Sumario: | 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 ∂ tu=∂ xxu+f(u). If f(u)=u p, 1<p≤3, we also obtain a law of large numbers for the explosion time. © 2012 Springer Science+Business Media New York. |
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