A method for identifying nonlinear terms in parabolic initial-boundary value problems
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The problem of identifying unknown nonlinear coefficients in a one dimensional diffusion equation is considered. It is shown that these coefficients can be recovered from "correct" overposed data. The main analytical tools used are the maximum principle and monotonicity, both of the underlying operator and of the overposed data. In some cases a naturally induced fixed point formulation results, while in other cases a collocation method is induced and this yields a unique piecewise linear function approximation to the undetermined coefficient. The results of some numerical simulations are given. © 1991.
author list (cited authors)
Pilant, M., & Rundell, W.