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Abstract:

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.

Registro:

Documento: Artículo
Título:A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time
Autor:Franco, T.; Groisman, P.
Filiación:Universidade Federal da Bahia, Salvador, Brazil
Departamento de Matemática, Fac. Cs. Exactas y Naturales, UBA and IMAS-CONICET, Buenos Aires, Argentina
Palabras clave:Blow-up; Hydrodynamic limit; Parabolic equations
Año:2012
Volumen:149
Número:4
Página de inicio:629
Página de fin:642
DOI: http://dx.doi.org/10.1007/s10955-012-0621-8
Título revista:Journal of Statistical Physics
Título revista abreviado:J. Stat. Phys.
ISSN:00224715
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224715_v149_n4_p629_Franco

Referencias:

  • Arnold, L., Theodosopulu, M., Deterministic limit of the stochastic model of chemical reactions with diffusion (1980) Adv. Appl. Probab, 12 (2), pp. 367-379
  • Bandle, C., Brunner, H., Blowup in diffusion equations: a survey (1998) J. Comput. Appl. Math, 97 (1-2), pp. 3-22
  • Blount, D., Comparison of stochastic and deterministic models of a linear chemical reaction with diffusion (1991) Ann. Probab, 19 (4), pp. 1440-1462
  • Blount, D., Law of large numbers in the supremum norm for a chemical reaction with diffusion (1992) Ann. Appl. Probab, 2 (1), pp. 131-141
  • Chen, X.Y., Uniqueness of the ω-limit point of solutions of a semilinear heat equation on the circle (1986) Proc. Jpn. Acad., Ser. A, Math. Sci, 62 (9), pp. 335-337
  • Chen, X.Y., Matano, H., Convergence, asymptotic periodicity, and finite-point blow-up in one-dimensional semilinear heat equations (1989) J. Differ. Equ, 78 (1), pp. 160-190
  • Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations (2002) Discrete Contin. Dyn. Syst, 8 (2), pp. 399-433. , Current developments in partial differential equations, Temuco (1999)
  • Kipnis, C., Landim, C., (1999) Scaling Limits of Interacting Particle Systems, 320. , Grundlehren der mathematischen Wissenschaften, Berlin: Springer
  • Kotelenez, P., Law of large numbers and central limit theorem for linear chemical reactions with diffusion (1986) Ann. Probab, 14 (1), pp. 173-193
  • Kotelenez, P., High density limit theorems for nonlinear chemical reactions with diffusion (1988) Probab. Theory Relat. Fields
  • Mourragui, M., Hydrodynamic limit for a jump, birth and death process (Limite hydrodynamique d'un processus de sauts, de naissances et de morts) (1993) C. R. Acad. Sci., Paris, Sér. I, 316 (9), pp. 921-924
  • Norris, J.R., (1998) Markov Chains, , Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge: Cambridge University Press
  • Pao, C.V., (1992) Nonlinear Parabolic and Elliptic Equations, , New York: Plenum Press
  • Quittner, P., Souplet, P., (2007) Superlinear Parabolic Problems, , Birkhäuser Advanced Texts: Basler Lehrbücher (Birkhäuser Advanced Texts: Basel Textbooks)Blow-up, global existence and steady states, Basel: Birkhäuser
  • Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1995) Blow-Up in Quasilinear Parabolic Equations, 19. , de Gruyter Expositions in MathematicsTranslated from the 1987 Russian original by Michael Grinfeld and revised by the authors, Berlin: de Gruyter
  • Vázquez, J.L., (2007) The Porous Medium Equation, , Oxford Mathematical MonographsMathematical theory, Oxford: Clarendon Press/Oxford University Press
  • Velázquez, J.J.L., Local behaviour near blow-up points for semilinear parabolic equations (1993) J. Differ. Equ, 106 (2), pp. 384-415
  • Weissler, F.B., Semilinear evolution equations in Banach spaces (1979) J. Funct. Anal, 32 (3), pp. 277-296

Citas:

---------- APA ----------
Franco, T. & Groisman, P. (2012) . A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time. Journal of Statistical Physics, 149(4), 629-642.
http://dx.doi.org/10.1007/s10955-012-0621-8
---------- CHICAGO ----------
Franco, T., Groisman, P. "A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time" . Journal of Statistical Physics 149, no. 4 (2012) : 629-642.
http://dx.doi.org/10.1007/s10955-012-0621-8
---------- MLA ----------
Franco, T., Groisman, P. "A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time" . Journal of Statistical Physics, vol. 149, no. 4, 2012, pp. 629-642.
http://dx.doi.org/10.1007/s10955-012-0621-8
---------- VANCOUVER ----------
Franco, T., Groisman, P. A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time. J. Stat. Phys. 2012;149(4):629-642.
http://dx.doi.org/10.1007/s10955-012-0621-8