Long time existence for the heat equation with a noise term
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We consider the equationu t =u xx +u γ W forx on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided 1 ≧γ<3/2.
KeywordsBoundary Condition Stochastic Process White Noise Probability Theory Mathematical Biology
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