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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Detalles Bibliográficos
Autor principal: Groisman, Pablo Jose
Publicado: 2012
Materias:
Blow-up
Hydrodynamic limit
Parabolic equations
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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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00224715_v149_n4_p629_Franco
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spelling paper:paper_00224715_v149_n4_p629_Franco2023-06-08T14:50:55Z A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time Groisman, Pablo Jose Blow-up Hydrodynamic limit Parabolic equations 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. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Blow-up
Hydrodynamic limit
Parabolic equations
spellingShingle Blow-up
Hydrodynamic limit
Parabolic equations
Groisman, Pablo Jose
A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
topic_facet Blow-up
Hydrodynamic limit
Parabolic equations
description 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.
author Groisman, Pablo Jose
author_facet Groisman, Pablo Jose
author_sort Groisman, Pablo Jose
title A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_short A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_full A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_fullStr A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_full_unstemmed A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
title_sort particle system with explosions: law of large numbers for the density of particles and the blow-up time
publishDate 2012
url 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
work_keys_str_mv AT groismanpablojose aparticlesystemwithexplosionslawoflargenumbersforthedensityofparticlesandtheblowuptime
AT groismanpablojose particlesystemwithexplosionslawoflargenumbersforthedensityofparticlesandtheblowuptime
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