| EPSRC Reference: |
EP/J011487/1 |
| Title: |
Singular limits of nonlinear elliptic and parabolic PDE |
| Principal Investigator: |
Crooks, Professor E |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
College of Science |
| Organisation: |
Swansea University |
| Scheme: |
Standard Research |
| Starts: |
27 April 2012 |
Ends: |
26 July 2012 |
Value (£): |
9,288
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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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| Related Grants: |
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| Panel History: |
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Summary on Grant Application Form |
Strong-competition limits of competing-population systems with two components
have proved an effective way of obtaining information about the competition
system for large values of the competition parameter. Understanding the
dynamics of such systems is very difficult in general, due to their lack of
variational structure. On the other hand, the strong-interaction limit is a scalar
equation which has a Lyapunov function and is much more easily studied.
Such singular limits are both mathematically useful, and correspond to the important
biological and physical phenomena of spatial segregation and phase separation.
For competition systems with more than two components, however, the techniques
that are effective in the two-component case fail and new ideas are needed.
Some success has been had been recently, using tools from free-boundary problems,
to show convergence of solutions of the competition system to a solution of a limit
problem.
The central goal of this proposal is to prove results on the so-called converse problem for
multi-component systems; that is, on whether or not a solution of the limit problem
does in fact arise as the limit of solutions of the original system. Such converse problems
are an essential and important part of the understanding of any singular limit, and have
yet to be addressed at all for strong-competition limits of multi-component systems.
We also aim to prove results on the converse problem for competition systems of
two components when the interaction terms are large only on a subdomain, and for
systems with a different, cubic type of competitive coupling, which occurs in modelling
certain quantum mechanical systems.
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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.swan.ac.uk |