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 stong law of large numbers for t...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2012 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/19892 |
| Online Access: | http://hdl.handle.net/11336/19892 |
| Access Level: | Open access |
| Keyword: | Hydrodinamic limit Blow-up Reaction-diffusion equation Particle system https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Summary: | 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 ∂tu = ∂xxu + f(u). If f(u) = u p , 1 < p ≤ 3, we also obtain a law of large numbers for the explosion time. |
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