| EPSRC Reference: |
EP/D052459/1 |
| Title: |
Exponential asymptotics for integro-differential equations |
| Principal Investigator: |
Crowdy, Professor DG |
| Other Investigators: |
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| Project Partners: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Mathematics Small Grant PreFEC |
| Starts: |
18 March 2006 |
Ends: |
17 September 2006 |
Value (£): |
10,140
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Mathematical Analysis |
| 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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A large number of physical problems involve the influence of ``small'' effects. An example is the effect of surface tension at the interface between two viscous fluids of differing viscosities. While apparently ``small'', such effects can often be surprisingly influential in determining global dynamical properties of the system. Since the effect is small, mathematically it is natural to attempt an asymptotic expansion in the parameter governing its influence on the problem.However, in many cases, standard asymptotic analysis fails and one has to examine exponentially small terms in order to ascertain the global effect of the small perturbation. This subject of ``exponential asymptotics'' has become a very active field of applied mathematics.Recent work, however, has focussed on rendering many of the mathematical ideas more rigorous. This proposal seeks to continue with the task of putting the subject of exponential asymptotics, especially as it pertains to the analysis of integro-differential equations, on a more rigorous footing. An initial case study, consisting of the selection problem for the rising Taylor bubble, will be analysed.
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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 |