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Exponential estimate for reaction diffusion models
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  • Published: October 1996

Exponential estimate for reaction diffusion models

  • Claudio Landim1 &
  • M. Eulália Vares1 

Probability Theory and Related Fields volume 106, pages 151–186 (1996)Cite this article

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Summary.

We consider the superposition of a speeded up symmetric simple exclusion process with a Glauber dynamics, which leads to a reaction diffusion equation. Using a method introduced in [Y] based on the study of the time evolution of the H −1 norm, we prove that the mean density of particles on microscopic boxes of size N α, for any 12/13<α<1, converges to the solution of the hydrodynamic equation for times up to exponential order in N, provided the initial state is in the basin of attraction of some stable equilibrium of the reaction–diffusion equation. From this result we obtain a lower bound for the escape time of a domain in the basin of attraction of the stable equilibrium point.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, CEP 22460 Jardim Botanico, Rio de Janeiro, Brazil (e-mail: Landim@ impa.br) , , , , , , BR

    Claudio Landim & M. Eulália Vares

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  1. Claudio Landim
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  2. M. Eulália Vares
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Received: 3 March 1995 / In revised form: 2 February 1996

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Landim, C., Vares, M. Exponential estimate for reaction diffusion models. Probab Theory Relat Fields 106, 151–186 (1996). https://doi.org/10.1007/s004400050061

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  • Issue Date: October 1996

  • DOI: https://doi.org/10.1007/s004400050061

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  • Mathematics Subject classification (1991): 60K35
  • 82A05
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