Solving inverse problems for PDEs in terms of Lax-Milgram functional and a generalized collage method
Davide La Torre Prof. , University of Milan
Herb Kunze Prof., University of Guelph, Ontario, Canada
Ed Vrscay Prof., University of Waterloo, Ontario, Canada
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ABSTRACT:
In this paper, we develop a general collage coding framework for inverse
problems in partial differential equations (PDEs) with boundary conditions.
Although a general PDEs inverse problem can be very complicated, via the Generalized Collage
Theorem in this paper, many such problems can be reduced to an optimization
problem which can be solved at least approximately.
We study a general theory for
variational formulation of PDEs and then
we show an application to a one-dimensional
steady-state diffusion equation.
We give many numerical examples and we analyze stability results under
perturbation of data.
SUGGESTED CITATION:
Davide La Torre Prof. , Herb Kunze Prof., and Ed Vrscay Prof.,
"Solving inverse problems for PDEs in terms of Lax-Milgram functional and a generalized collage method"
(May 2006).
UNIMI - Research Papers in Economics, Business, and Statistics.
Statistics and Mathematics.
Working Paper 9.
http://services.bepress.com/unimi/statistics/art9
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