Results 1 
3 of
3
Invariant manifold reduction and bifurcation for stochastic partial differential equations
 Linearization of Random Dynamical Systems. Dynamics Report, Volumn 4. SpringVerlog
, 1995
"... Abstract. Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is prove ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Abstract. Stochastic partial differential equations arise as mathematical models of complex multiscale systems under random influences. Invariant manifolds often provide geometric structure for understanding stochastic dynamics. In this paper, a random invariant manifold reduction principle is proved for a class of stochastic partial differential equations. The dynamical behavior is shown to be described by a stochastic ordinary differential equation on an invariant manifold, under suitable conditions. The change of dynamical structures for the stochastic partial differential equations is thus obtained by investigating the stochastic ordinary differential equation. The random cone invariant property is used in the approach. Moreover, the invariant manifold reduction principle is applied to detect bifurcation phenomena and stationary states in stochastic parabolic and hyperbolic partial differential equations. 1.
Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity
, 2009
"... The qualitative properties of local random invariant manifolds for stochastic partial differential equations with quadratic nonlinearities and multiplicative noise is studied by a cut off technique. By a detail estimates on the Perron fixed point equation describing the local random invariant manifo ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The qualitative properties of local random invariant manifolds for stochastic partial differential equations with quadratic nonlinearities and multiplicative noise is studied by a cut off technique. By a detail estimates on the Perron fixed point equation describing the local random invariant manifold, the structure near a bifurcation is given. 1 1