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Connection between the Burgers equation with an elastic forcing term and a stochastic process

Abstract

We present a complete analytical resolution of the one dimensional Burgers equation with the elastic forcing term κ2x+f(t)-\kappa^{2} x+f(t), κR\kappa\in\mathbb{R}. Two methods existing for the case κ=0\kappa=0 are adapted and generalized using variable and function transformations, valid for all values of space an time. The emergence of a Fokker-Planck equation in the method allows to connect a fluid model, depicted by the Burgers equation, with an Ornstein-Uhlenbeck process

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