A phase transition for a stochastic PDE related to the contact process
A phase transition for a stochastic PDE related to the contact process
复制标题
与接触过程相关的随机偏微分方程的相变
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
R. Tribe
中科院分区：
文献类型：
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作者：
C. Mueller;R. Tribe
摘要我们考虑具有半线性项和非线性白噪声项的一维热传导方程。R.Durrett猜想，这个方程是长程相互作用下接触过程的一个弱极限。我们证明了我们的方程存在相变。更准确地说，我们假设初始函数是总质量有界的非负函数。如果方程中的某个参数足够小，则解在有限时间内消失到0，概率为1。如果这个参数足够大，则解有一个永远不会消失到0的正概率。这一结果回答了杜雷特的一个问题。
SummaryWe 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.