| EPSRC Reference: |
GR/M45610/01 |
| Title: |
RANDOM LAGRANGIAN SYSTEMS AND BURGERS EQUATION |
| Principal Investigator: |
Khanin, Professor K |
| Other Investigators: |
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| Project Partners: |
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| Department: |
S of Mathematical and Computer Sciences |
| Organisation: |
Heriot-Watt University |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
31 March 2000 |
Ends: |
30 March 2001 |
Value (£): |
38,829
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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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 main aim of the proposed research is to study d-dimensional inviscid Burgers equation driven by random force using variational approach and methods of the theory of dynamical systems. These methods turned out to be very useful in one-dimensional case. The principal difference between the one-dimensional case a multi-dimensional situation is connected with much more complicated geometry of the shock waves of the latter. As a result, one-dimensional theory cannot be directly applied to the multi-dimensional case. Nevertheless, we plan to show that many of the crucial features are still valid in the multi-dimensional situation.We intend to construct stationary distribution for solutions of Burgers equation and study its properties. To do so, we plan to combine variational approach with the methods of the theory of dynamical systems. One of our main aims is to show that for generic random Lagrangian system on compact connected Riemannian manifold there exists a unique globally minimising orbit. We will then study hyperbolic properties of this orbit and relate them to the analysis of the stationary solutions of Burgers equation.
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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.hw.ac.uk |