| EPSRC Reference: |
GR/R40241/01 |
| Title: |
Wentzell Boundary Value Problems for Pseudo-Differential Operators with Negative Definite Symbols |
| Principal Investigator: |
Jacob, Professor N |
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| Department: |
Mathematics |
| Organisation: |
Swansea University |
| Scheme: |
Fast Stream |
| Starts: |
01 September 2001 |
Ends: |
30 April 2003 |
Value (£): |
62,890
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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For pseudo-differential operators q(x, DX, D Y) = Q(DY) + p(x, DX) considered on Rn x R+ Wentzell boundary valueproblems will be considered in order to construct extensions of - q(x, DX, Dy ) generating Feller or sub-Markoviansemigroups, hence Markov processes (Xt) (t>=0) with state space Rn x R+ . The operator Q(DY)will be either a fractionalderivative of order 1 < alpha < 2, of type f(- partial differential divided by partial differential of y) where f is an appropriate Bernstein function, or Q(eta) will be a more general continuous negative definite function. The operator p(x, Dx) has as symbol such that xi tends towards p(x, xi) is as a negative definite function without quadratic term. The corresponding process will be a jump-type process without diffusion. The difficulty is that almost all classical techniques for solving boundary value problems do not apply in our case as proved before. Fractional calculus and Wiener-Hopf factorisation might work.
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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 |
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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 |