IMAS 23417
INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Unidad Ejecutora - UE
artículos
Título:
A particle system with explosions: law of large numbers for the density of particles and the blow-up time
Autor/es:
FRANCO, TERTULIANO; GROISMAN, PABLO
Revista:
JOURNAL OF STATISTICAL PHYSICS
Editorial:
SPRINGER
Referencias:
Lugar: Berlin; Año: 2012 vol. 194 p. 629 - 642
ISSN:
0022-4715
Resumen:
Consider a system of independent random walks in the discrete torus withcreation-annihilation of particles and possible explosion of thetotal 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 thesupremum norm. The limiting object is a classical solution to the semilinearheat equation $\p_t u=\p_{xx} u + f(u)$. If $f(u)=u^p$, $1<p\leq 3$, we also obtain a law of large numbers for the explosion time.
