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Consider the stochastic partial differential equation u t = u xx + u γ W, where x E I ≡ [0, J], W = W(t, x) is 2-parameter white noise, and we assume that the initial function u(0, x) is nonnegative and not identically 0. We impose Dirichlet boundary conditions on u in the interval I. We say that u blows up in finite time, with positive probability, if there is a random time T 0./t↑T x It was known that if y 3/2, then there is a positive probability that u blows up in finite time.

The critical parameter for the heat equation with a noise term to blow up in finite time