On the invariant symmetries of the ![[script D]](http://scitation.aip.org/servlet/GetImg?key=JMAPAQ000048000010102504000001%3A0%3A0%3A28&t=a&d=a)
-metrics
We analyze the symmetries and other invariant qualities of the -metrics (type D aligned Einstein-Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-fr...
We analyze the symmetries and other invariant qualities of the -metrics (type D aligned Einstein-Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-fr...
Integrable boundary value problems for elliptic type Toda lattice in a disk
The concept of integrable boundary value problems for soliton equations on and + is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lat...
The concept of integrable boundary value problems for soliton equations on and + is extended to regions enclosed by smooth curves. Classes of integrable boundary conditions in a disk for the Toda lat...
A dynamical approximation for stochastic partial differential equations
J. Math. Phys. 48, 102701 (2007); doi:10.1063/1.2800164
Published 23 October 2007
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Random invariant manifolds provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential system on the random invariant manifold, under suitable conditions. As an application, stationary states (invariant measures) are considered for a class of stochastic hyperbolic partial differential equations.
©2007 American Institute of Physics
| History: | Received 10 May 2007; accepted 27 September 2007; published 23 October 2007 |
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0022-2488 (print)
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