Abstract
A problem of expansion of nonlinear waves in a heterogeneous media is considered, this problem is described by a Burgers equation with a stochastic right-hand side. Existence of a statistical solution is proved and sufficient conditions are obtained for such properties as uniformity (independence on translation) of the probability measure of the solution, stationarity and ergodicity.
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References
A. A. Arsen’ev, Statistical Solutions of a Linear Wave Equation, Preprint No. 81 (IPM AN SSSR, Moscow, 1978) [in Russian].
O. A. Oleinik, “Discouninuous Solutions to Nonlinear Differential Equations,” Uspekhi Matem. Nauk 12(3), 75 (1957).
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Original Russian Text © E.A. Lapshin, N.A. Pshenitsina, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 51–52.
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Lapshin, E.A., Pshenitsina, N.A. Existence and properties of a static solution to a nonhomogeneous Burgers equation. Moscow Univ. Math. Bull. 62, 242–243 (2007). https://doi.org/10.3103/S0027132207060058
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DOI: https://doi.org/10.3103/S0027132207060058