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The Burgers equation with a noisy force and the stochastic heat equation. (English) Zbl 0804.35158
As is well known, the classical Burgers equation can be reduced to the heat equation by means of the Cole-Hopf transformation. The authors extend this technique to tackle the Burgers equation with space-time white noise. Since the equation is nonlinear, a difficulty arises concerned with multiplication of distributions. This is overcome by interpreting the nonlinear term as Wick product.

35R60 PDEs with randomness, stochastic partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
Full Text: DOI
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[19] DOI: 10.1007/BFb0074920 · doi:10.1007/BFb0074920
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