| EPSRC Reference: |
GR/R90994/01 |
| Title: |
ANALYSIS OF NONLINEAR AND NONHOMOGENOUS DIFFUSIONS |
| Principal Investigator: |
Zegarlinski, Professor B |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 2002 |
Ends: |
28 February 2006 |
Value (£): |
156,801
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Mathematical Physics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The purpose of the project is to study the ergodicity properties of nonlinear as well as nonhomogenous semigroups for which the underlying space is infinite dimensional. Such cases are very important in applications (e.g. in statistical mechanics of nonhomogenous systems, supercondactivity, ecology, finance,...) and therefore it would be important to make a progress in their mathematical understanding, which is still quite poor. We would like to develop a method for controlling the ergodicity of dissipative dynamics and apply it to some important models (as e.g. d2!2 Heisenberg models with generalised Kawasaki dynamics and dynamics generated by infinite dimensional analogs of L_p Laplacians ). The idea of the method is based on application of coercive inequalities (as e.g. so called q- log Sobolev or generalised entropy bounds involving measures with non-Gaussian tails), use of duality transformation and scaling properties of the system together with decomposition of the dynamics with respect to a sequence of a-algebras. The problem is not only mathematically challenging and interesting. Because the nonlinear as well as hypoelliptic dynamics are very common in many applications, it would be clearly important to make progress in understanding them.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.imperial.ac.uk |