STATISTICS OF SHOCKS IN SOLUTIONS OF INVISCID BURGERS-EQUATION

被引：175

作者：

SINAI, YG ^{[1
]}

机构：

[1] PRINCETON UNIV,DEPT MATH,PRINCETON,NJ 08544

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1992年 / 148卷 / 03期

关键词：

D O I：

10.1007/BF02096550

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The purpose of this paper is to analyze statistical properties of discontinuities of solutions of the inviscid Burgers equation having a typical realization b(y) of the Brownian motion as an initial datum. This case was proposed and studied numerically in the companion paper by She, Aurell and Frisch. The description of the statistics is given in terms of the behavior of the convex hull of the random process w(y) = integral-y/0 (b(eta) + eta) d-eta. The Hausdorff dimension of the closed set of those y where the convex hull coincides with w is also studied.

引用

页码：601 / 621

页数：21

共 6 条

[1]

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[2]

Falconer, 1985, GEOMETRY FRACTAL SET

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COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1950, 3 (03) :201-230

[4] THE INVISCID BURGERS-EQUATION WITH INITIAL DATA OF BROWNIAN TYPE [J].

SHE, ZS ;

AURELL, E ;

FRISCH, U .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 148 (03) :623-641

[5]

SINAI YG, 1992, IN PRESS THEOR MATH

[6]

STROOCK DW, 1979, MULTIDIMENSIONAL DIF, P338

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