Mathematical Sciences: Determination of Nonlinear Terms in  Parabolic and Elliptic Partial Differential Equations and   Overposed Data
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
The aim of this project is to investigate certain inverse problems          for elliptic and parabolic partial differential equations that contain          unknown coefficients which are functions of the dependent variables.            These coefficients can be recovered by giving overposed boundary data,          that it prescribed Dirichlet   type data and a chosen curve lying on            the boundary region. The method consists of converting the inverse              problem into a fixed-point problem in which one has a mapping from the          unknown coefficients to the overposed data. The fixed point problem is          solved through an iteration scheme. The authors have been able to               demonstrate the convergence of that scheme in some cases. They propose          now a number of research questions to be investigated to  improve the           knowledge of the technique.                                                         The inverse problems arise in a number of applications where one            has observed data and the problem is to find the parameters of the              equation describing the phenomenon. Continuum mechanics,   mathematical         biology and chemical combustion theory are among potential applications         of this inverse method.
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[{'Code': '126600', 'Text': 'APPLIED MATHEMATICS'}, {'Code': '239800', 'Text': None}]
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