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title:
A Nonlinear Parameter Identification Problem involving a Parabolic Differential Equation |
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name:
Ressel |
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first name:
Rudolf
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location/conference:
SPP-JT11
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PRESENTATION-link:
http://www.dfg-spp1324.de/nuhagtools/event_NEW/dateien/SPP-JT11/talks/SPP-JT2011_03_ressel.pdf |
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abstract:
We are concerned with identifying certain parameters in a parabolic reaction-diffusion equation from measured data. The PDE describes the gene concentrations in embryos at an early state of development.
he forward problem is formulated as an evolution equation, and the analytical properties of the parameter-to-state operator are analyzed. The results justify the application of an iterated soft-shrinkage algorithm within a Tikhonov regularization approach. The forward problem is treated by means of a new adaptive wavelet algorithm which is based on tensor wavelets. An implementation of this procedure involving the new adaptive wavelet solver is proposed and numerical results are presented, yielding a proof of concept.
The talk is based on joint work with Ulrich Friedrich. |
