Details of Grant 

EPSRC Reference:	EP/C520335/1
Title:	Dynamical aspects of stochastic partial differential equations
Principal Investigator:	Zhang, Professor T
Other Investigators:	Zhao, Professor H
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Manchester, The
Scheme:	Mathematics Small Grant PreFEC
Starts:	01 March 2005	Ends:	31 August 2005	Value (£):	10,252
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
Stochastic partial differential equations (SPDEs) arise in many physical problems such as neuron sciences, mathematical biology, fluid dynamics, geophysics, plasma physics etc. To understand the long time behaviour of solution is one of the most important problems in random dynamical systems. Invariant manifolds is a useful characterization of the local behaviour. Invariant measures represent the weak convergence of the solution. In this proposal, we propose to study the pathwise convergence and long time behaviour of solutions of SPDEs. Following our recent breakthrough on existence of semiflows of stochastic partial differential equations and stochastic evolution equations (references 11 and 12), the proposed research is to study the pathwise local behaviour of SPDEs near a stationary solution and the global structutre of some more specific SPDEs and stochastic reaction diffusion equations, existence of the stationary solutions, Lyapunov exponents, and extend these results to more SPDEs such as when the noise is of (linear/nonlinear) multiplicative type. We will study the existence of the stationary solutions by studying the integral equations that we have recently observed in reference 12. These are fundamental problems in stochastic dynamical systems. The SPDEs that we proposed to study include some well-known equations such as stochastic KPP equations, stochastic Ginzbargh-Landan equation, stochastic Chafee-Infante equations, stochastic Burgers equations and stochastic Navier-Stokes equations. These equations arised in real physical problems.
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Organisation Website:	http://www.man.ac.uk