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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00224715_v149_n4_p629_Franco |
| Aporte de: |
| 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 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. |
|---|