For more information about this meeting, contact Jinchao Xu.
| Title: | Multi-scale approach to evolution equations with applications |
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| Seminar: | Computational and Applied Mathematics Colloquium |
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| Speaker: | Maarten de Hoop (Purdue) |
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| Abstract: |
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| Wave-equation imaging and wave-equation (reflection) tomography can
essentially be expressed in terms of solving particular evolution
equations. The underlying model describes the single scattering of
waves off discontinuities in a background medium. Here, we are
concerned with developing a method that admits background media of
limited smoothness, which leads to evolution equations generated by
certain pseudodifferential operators. We develop a multi-scale
approach to solving such evolution equations, while making use of
solution representations based on curvelets. We discuss results
concerning the `concentration' of curvelets. We then discuss an
approximation of functions following the dyadic parabolic
decomposition that leads to sparse representations of initial data,
image, and solutions irrespective of scale. Finally, we mention the
existence and construction of Fr\'{e}chet derivatives, with respect to
the background medium, of the solution operators associated with the
evolution equations.
Joint research with F. Andersson, M. Carlsson, H. Smith and G. Uhlmann. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 11 / 09 / 2007 |
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| Time: | 03:35pm - 04:25pm |
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