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1994•Communications in Partial Differential EquationsOpen access

The burgers equation with a noisy force and the stochastic heat equation

Helge Holden, Tom Lindstrøm, Bernt Øksendal, Jan Ubøe, T.S. Zhang

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Abstract

We consider the multidimensional Burgers equation with a viscosity term and a random force modelled by a functional of time-space white noise, Wick products. Then we show that the nonlinear equation (B) can be transformed into a linear, stochastic heat equation with a noisy potential. This heat equation is solved explicitly in the following two cases.

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What this paper is about

We consider the multidimensional Burgers equation with a viscosity term and a random force modelled by a functional of time-space white noise, Wick products. Then we show that the nonlinear equation (B) can be transformed into a linear, stochastic heat equation with a noisy potential. This heat equation is solved explicitly in the following two cases.

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Available abstract

We consider the multidimensional Burgers equation with a viscosity term and a random force modelled by a functional of time-space white noise, Wick products. Then we show that the nonlinear equation (B) can be transformed into a linear, stochastic heat equation with a noisy potential. This heat equation is solved explicitly in the following two cases.

Key concepts: Burgers' equation, Heat equation, Mathematics, White noise, Mathematical analysis, Nonlinear system, Viscosity, Space (punctuation)

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