A phase transition for a stochastic PDE related to the contact process View Full Text


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Article Info

DATE

1994-06

AUTHORS

Carl Mueller, Roger Tribe

ABSTRACT

We consider the one-dimensional heat equation, with a semilinear term and with a nonlinear white noise term. R. Durrett conjectured that this equation arises as a weak limit of the contact process with longrange interactions. We show that our equation possesses a phase transition. To be more precise, we assume that the initial function is nonnegative with bounded total mass. If a certain parameter in the equation is small enough, then the solution dies out to 0 in finite time, with probability 1. If this parameter is large enough, then the solution has a positive probability of never dying out to 0. This result answers a question of Durett. More... »

PAGES

131-156

References to SciGraph publications

  • 1993-09. Blowup for the heat equation with a noise term in PROBABILITY THEORY AND RELATED FIELDS
  • 1986. An introduction to stochastic partial differential equations in ÉCOLE D'ÉTÉ DE PROBABILITÉS DE SAINT FLOUR XIV - 1984
  • 1993-03. White noise driven SPDEs with reflection in PROBABILITY THEORY AND RELATED FIELDS
  • 1992-03. Comparison methods for a class of function valued stochastic partial differential equations in PROBABILITY THEORY AND RELATED FIELDS
  • 1991. A New Method for Proving the Existence of Phase Transitions in SPATIAL STOCHASTIC PROCESSES
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01199262

    DOI

    http://dx.doi.org/10.1007/bf01199262

    DIMENSIONS

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