We consider numerical algorithms for identifying coefficients
in parabolic equations from over specified boundary data.
More precisely we are interested in approximating the thermal
diffusivity $a(x)$, for 0
measurements on the boundary, i.e. along the lines x=0 and x=L.
The numerical identification of this coefficient is a severely
ill--posed problem, which is difficult to solve. In general
temperature and heat--flux data on the boundary does not provide
enough information for determining the solution uniquely. Thus it
is important to include a priori information regarding the thermal
diffusivity a(x), that we want to calculate, and also to make
sure that the actual boundary data that are imposed are
appropriately chosen.
The problem of identifying coefficents in differential equations
appear in several applications. We discuss potential applications and
present both numerical algorithms, and computational results.
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