Long time existence for the heat equation with a noise term (Q806166)
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scientific article; zbMATH DE number 4205534
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Long time existence for the heat equation with a noise term |
scientific article; zbMATH DE number 4205534 |
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Long time existence for the heat equation with a noise term (English)
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1991
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We consider the equation \(u_ t=u_{xx}+u^{\gamma}\dot W\) for x on a finite interval, with Dirichlet boundary conditions. \(\dot W\) is spacetime white noise. The initial condition is continuous and nonnegative. We show existence and uniqueness for all time, provided \(1\leq \gamma <3/2\).
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two-parameter white noise
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density of super-Brownian motion
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Dirichlet boundary conditions
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existence and uniqueness
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