| EPSRC Reference: |
GR/K96342/01 |
| Title: |
TRAVELLING WAVES FOR REACTION-DIFFUSION SYSTEMS |
| Principal Investigator: |
Toland, Professor JF |
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| Department: |
Mathematical Sciences |
| Organisation: |
University of Bath |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 September 1996 |
Ends: |
30 November 1999 |
Value (£): |
113,445
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| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
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Summary on Grant Application Form |
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The proposed research is in the mathematical theory of nonlinear parabolic systems with particular emphasis on travelling wave theory. Following recent success in the study of intermediate zeros for bi-stable systems there is a need to develop analogous theory for mono-stable systems. Further, recent extensions of topological theory to gradient-dependent bi-stable systems highlight the need for the analogous extension to mono-stable systems. Generalisations to gradient-dependent bi-stable systems of results obtained on the existence of chains of heteroclinic orbits will also be sought. (This development involves the extension to gradient-dependent, mono-stable systems of existing gradient independent theory). These new developments for gradient-dependent systems mean that the global well-posedness for the corresponding initial-value problem must now be addressed.In addition, it is proposed to study the general question of uniqueness of monotone solutions both as monotone solutions and in the class of all solutions. The question of the size and sign of the travelling-wave velocity will be examined, as will the possible extensions of these theories to systems in higher space dimensions. All the questions posed have their origins in problems which arise frequently and naturally in problems from biology.
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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.bath.ac.uk |