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
Autores principales: Franco, T., Groisman, P.
Formato: JOUR
Materias:
Blow-up
Hydrodynamic limit
Parabolic equations
Acceso en línea: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
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spelling todo:paper_00224715_v149_n4_p629_Franco2023-10-03T14:32:57Z A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time Franco, T. Groisman, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Franco, T.
Groisman, P.
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.
format JOUR
author Franco, T.
Groisman, P.
author_facet Franco, T.
Groisman, P.
author_sort Franco, T.
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
url http://hdl.handle.net/20.500.12110/paper_00224715_v149_n4_p629_Franco
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AT groismanp aparticlesystemwithexplosionslawoflargenumbersforthedensityofparticlesandtheblowuptime
AT francot particlesystemwithexplosionslawoflargenumbersforthedensityofparticlesandtheblowuptime
AT groismanp particlesystemwithexplosionslawoflargenumbersforthedensityofparticlesandtheblowuptime
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