Transport equations for a general class of evolution equations with randomperturbations

Authors
Citation
Mz. Guo et Xp. Wang, Transport equations for a general class of evolution equations with randomperturbations, J MATH PHYS, 40(10), 1999, pp. 4828-4858
Citations number
9
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
40
Issue
10
Year of publication
1999
Pages
4828 - 4858
Database
ISI
SICI code
0022-2488(199910)40:10<4828:TEFAGC>2.0.ZU;2-T
Abstract
We derive transport equations from a general class of equations of form iu( t) = H(X,D)u + V(X,D)u where H(X,D) and V(X,D) are pseudodifferential opera tors (Weyl operator) with symbols H(x,k) and V(x,k), where H(x,k) being pol ynomial in k and smooth in x,V(x,k) is a mean zero random function and is s tationary in space variable. We also consider system of equations in the ab ove form. Such equations cover many of the equations that arise in wave pro pagations, such as those considered in a paper by Ryzhik, Papanicolaou, and Keller [Wave Motion 24, 327-370 (1996)]. Our results generalize those by R yzhik, Papanicolau, and Keller. (C) 1999 American Institute of Physics. [S0 022-2488(99)03209-0].