Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity
نویسندگان
چکیده
منابع مشابه
Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity
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.
متن کاملAmplitude Equations for Spdes: Approximate Centre Manifolds and Invariant Measures
We review recent results on the approximation of transient dynamics of SPDEs by amplitude equations. As an application we derive the flow along an approximate centre manifold, and we study the dynamics of random fixed points. To discuss the long-time behaviour we give an approximation result for invariant measures.
متن کاملMultiscale Analysis for SPDEs with Quadratic Nonlinearities
In this article we derive rigorously amplitude equations for stochastic PDEs with quadratic nonlinearities, under the assumption that the noise acts only on the stable modes and for an appropriate scaling between the distance from bifurcation and the strength of the noise. We show that, due to the presence of two distinct timescales in our system, the noise (which acts only on the fast modes) g...
متن کاملAmplitude equation for SPDEs with quadratic nonlinearities∗
In this paper we rigorously derive stochastic amplitude equations for a rather general class of SPDEs with quadratic nonlinearities forced by small additive noise. Near a change of stability we use the natural separation of time-scales to show that the solution of the original SPDE is approximated by the solution of an amplitude equation, which describes the evolution of dominant modes. Our res...
متن کاملParametrisation of Local Invariant Manifolds
We present a method to compute enclosures of the local invariant manifolds of a hyperbolic saddle of an analytic vector eld. By considering parametrisations of the invariant manifolds, instead of describing them as graphs of functions from the corresponding tangent spaces, we nd simple recursive formulae for their Taylor coe cients. In addition to this, we obtain rigorous bounds on the remainde...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2009
ISSN: 1040-7294,1572-9222
DOI: 10.1007/s10884-009-9145-6