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 Kwapien and Woyczynski.
Publié le : 1994-08-14
Classification:
Stochastic Burgers' flow,
domination principle,
Schur convexity,
maximum energy density,
60H15,
35K55,
76F99
@article{1177004974,
author = {Hu, Yiming and Woyczynski, W. A.},
title = {An Extremal Rearrangement Property of Statistical Solutions of Burgers' Equation},
journal = {Ann. Appl. Probab.},
volume = {4},
number = {4},
year = {1994},
pages = { 838-858},
language = {en},
url = {http://dml.mathdoc.fr/item/1177004974}
}
Hu, Yiming; Woyczynski, W. A. An Extremal Rearrangement Property of Statistical Solutions of Burgers' Equation. Ann. Appl. Probab., Tome 4 (1994) no. 4, pp. 838-858. http://gdmltest.u-ga.fr/item/1177004974/