THE BURGERS-EQUATION UNDER DETERMINISTIC AND STOCHASTIC FORCING

The forced Burgers equation is linearized and investigated in the case when the forcing is the product of a distribution (a derivative of a dirac delta function) multiplied by an arbitrary function of time: G(x , t) = delta'(x)F(t). In the case when F(t) is a deterministic functio n of time, explicit solutions are obtained and the asymptotic behaviou r is analyzed for different choices of F(t). The case when F(t) is ran dom Gaussian noise and weakly correlated, is also analyzed. Explicit e xpressions are obtained for the statistical average of the solution an d for some relevant correlation functions. In the large time and long wavelength limit, the two-time correlation function of the system, exh ibits a scaling behaviour of diffusive type.