| EPSRC Reference: |
GR/R60157/01 |
| Title: |
Second order parabolic partial differential equations on Riemannian manifolds |
| Principal Investigator: |
Grigor'Yan, Professor A |
| Other Investigators: |
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| Department: |
Mathematics |
| Organisation: |
Imperial College London |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 April 2002 |
Ends: |
31 March 2005 |
Value (£): |
145,042
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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This proposal is devoted to studying qualitative and quantitative properties of fundamental solutions of second order parabolic equations, including those on Riemannian manifolds. The following problems will be investigated:1. Upper and lower bounds for heat kernel of a parabolic Schrodinger equation on a complete Riemannian manifold. The main direction of the research here is to reveal the relations between the Riemannian geometry and the potential on the one side, and the long time and long distance heat kernel behaviour on the other side.2. Gaussian pointwise estimates of fundamental solutions for parabolic equations with time-dependent coefficients. The main direction here is to develop a time-dependent perturbation theory for parabolic equations.3. Regularity of solutions of parabolic equations with time-dependent measurable coefficients. The main direction here is to obtain optimal conditions on the lower order terms, which would guarantee certain regularity of the solutions (such as continuity, a Holder continuity, and differentiability).
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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 |