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Zbl 0805.60053
Hu, Yiming; Woyczyński, W.A.
An extremal rearrangement property of statistical solutions of Burgers' equation.
(English)
[J] Ann. Appl. Probab. 4, No.3, 838-858 (1994). ISSN 1050-5164

Summary: We prove that a certain (centered unimodal) rearrangement of coefficients in the moving average initial input process maximizes the variance (energy density) of the limit distribution of the spatiotemporal random field solution of a nonlinear partial differential equation called Burgers' equation. Our proof is in the spirit of domination principles developed in the book by {\it S. Kwapień} and {\it W. A. Woyczyński} [Random series and stochastic integrals: Single and multiple (1992; Zbl 0751.60035)].
MSC 2000:
*60H15 Stochastic partial differential equations
35K55 Nonlinear parabolic equations
76F99 Turbulence

Keywords: Schur convexity; maximum energy density; Burgers' equation; domination principles

Citations: Zbl 0751.60035

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