| EPSRC Reference: |
GR/R69518/01 |
| Title: |
Asymptotics with Caustics and Stochastic Reaction Diffusion Equations |
| Principal Investigator: |
Zhao, Professor H |
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| Department: |
School of Mathematics |
| Organisation: |
Loughborough University |
| Scheme: |
Fast Stream |
| Starts: |
30 September 2002 |
Ends: |
29 September 2005 |
Value (£): |
62,266
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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In this project, we propose to examine the qualitative and asymptotic behaviour of solutions of certain reaction diffusion and other equations in the presence of caustics, and random travelling waves and stability of stationary solutions for certain nonlinear stochastic reaction diffusion equations. A principal tool will be stochastic elementary formula pioneered by Elworthy and Truman studying detailed asymptotics of the solutions to heat equations under a no-caustic condition. Ever since the proof of this important result, the problem of the stochastic elementary formula on caustics has remained as one of the difficult and important problems in stochastic methods for reaction diffusion equations and is still open. In this project we will solve the problem and give detailed asymptotics for the solutions at and beyond the caustic, and investigate its applications in many other problems. Following our new results on the ergodic and pathwise property of stochastic KPP equations, we will be able to use this method to study the random travelling waves of stochastic reaction diffusion equations thoroughly e.g. for random initial conditons, space dependaent white noise and systems of stochastic reation diffusion equations. In particular, we will be able to give a detailed analysis of the solution at and near the wave front. To carry the analysis further, we will prove a stable and unstable manifold theorem for certain nonlinear stochastic reaction diffusion equations.
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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.lboro.ac.uk |