Abstract
We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, known as the Burgers’ equation, under stochastic initial conditions which are assumed to be of the shot noise type. In contrast to the previous work by (1991), a non-Gaussian scaling limit of the statistical solutions is discovered. The Burgers’ equation is known to descibe various physical phenomena such as nonlinear and shock waves. In view of the inelastic type of particles’ collisions, the Burgers’ equation (or more precisely its vector version) coupled with the continuity equation has been also studied as a model of evolution of distribution the selfgravitating matter. Thus, information about the time dependence of the initial fluctuations is epected to yield a theoretical model for the observed large scale structure of the universe (see (1989) and (1992)).A survey of stochastic Burgers’ flows can be found in (1993).
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Surgailis, D., Woyczyński, W.A. (1993). Long Range Prediction and Scaling Limit for Statistical Solutions of The Burgers’ Equation. In: Fitzmaurice, N., Gurarie, D., McCaughan, F., Woyczyński, W.A. (eds) Nonlinear Waves and Weak Turbulence. Progress in Nonlinear Differential Equations and Their Applications, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0331-5_16
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DOI: https://doi.org/10.1007/978-1-4612-0331-5_16
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