| EPSRC Reference: |
GR/R18642/01 |
| Title: |
Expnential Asymptotics For Evolutionary Systems |
| Principal Investigator: |
Howls, Professor CJ |
| Other Investigators: |
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| Project Partners: |
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| Department: |
School of Mathematics |
| Organisation: |
University of Southampton |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
04 October 2001 |
Ends: |
03 October 2004 |
Value (£): |
161,876
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| EPSRC Research Topic Classifications: |
| Mathematical Analysis |
Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| Manufacturing |
No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Techniques of asymptotics beyond all orders (whereby crucial exponentially small terms, 'hidden' beyond a divergent algebraic series in the small parameter, are extracted) will be extended to time-dependent nonlinear problems. The ground for this will first be prepared by studying in tandem (I) steady (travelling wave) formulations of moving boundary problems not amenable to existing approaches and (II) Linear time-dependent problems, constructive methods currently being largely absent even in the linear case. Nonlinear evolution equations and genuinely time-dependent moving boundary problems will then be addressed. This will require complementary categorisation of the effects of time-dependent singularity bifurcations on the exponential asymptotics. The resulting theory will then be subjected to numerical experimentation and validation. The field is one in which genuinely constructive, and widely effective, methods are currently entirely lacking; it is the central area in asymptotic methods of which this is the case. The challenge will be met by bringing together a team of investigators with the background and range of skills needed to achieve these ambitious goals.
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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.soton.ac.uk |