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...

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Detalles Bibliográficos
Autores: Tertuliano, Franco, Groisman, Pablo Jose
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/19892
Acceso en línea:http://hdl.handle.net/11336/19892
Access Level:acceso abierto
Palabra clave:Hydrodinamic limit
Blow-up
Reaction-diffusion equation
Particle system
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
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 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.