Details of Grant 

EPSRC Reference:	EP/J017418/1
Title:	On the long term behaviour of stochastic heat equations
Principal Investigator:	Foondun, Dr M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Sciences
Organisation:	Loughborough University
Scheme:	First Grant - Revised 2009
Starts:	15 October 2012	Ends:	14 October 2014	Value (£):	99,910
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 05 Mar 2012 Mathematics Prioritisation Panel Meeting March 2012 Announced
Summary on Grant Application Form
Many phenomena evolve under the influence of random inputs. For instance, the motion of a strand of DNA, the internal structure of the sun and many phenomena in particle systems all involve randomness. To model these situations, one can often use stochastic partial differential equations(SPDEs) which roughly speaking, describe motions which are under the influence of some kind of randomness. Compared with the theory of partial differential equations, the theory of SPDEs is not well developed. Fortunately, this situation is changing quite rapidly; a lot of researchers have been studying SPDEs during the past decades and some major advances have been made. The foundations of the subject have been settled and one has the option of three different approaches; the Hilbert space approach, the martingale measure approach and the L_p space approach. The main aim of this proposal is to study the long term behaviour of a wide class of stochastic differential equations. More precisely, we propose to study a phenomenon called "intermittency" whereby for large times, the solutions of the SPDE have high peaks. Intermittency is actively studied in the special case where space is assumed to be a discrete lattice and so far only a small number of continuous space equations have been proved to exhibit this phenomenon. This proposal aims to show that a much wider class of SPDEs exhibit these kinds of behaviour. This will shed light on a lot of phenomena which involve randomness.
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Organisation Website:	http://www.lboro.ac.uk