We study the identification of the nonlinearities A,(→)b and c appearing in the quasilinear parabolic equation y_t − div(A(y)∇y + (→)b(y)) + c(y) = u inΩ × (0,T), assuming that the solution of an associated boundary value problem is known at the terminal time, y(x,T), over a (probably small) subset of Ω, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A,(→)b and c is proved under appropriate assumptions. Secondly, we consider a finite-dimensional optimization problem that allows for the reconstruction of the nonlinearities. Some numerical results in the one-dimensional case are presented, even in the case of noisy data.
@article{bwmeta1.element.bwnjournal-article-amcv11i4p859bwm,
author = {Fern\'andez, Luis a. and Pola, Cecilia},
title = {Identification of a quasilinear parabolic equation from final data},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {11},
year = {2001},
pages = {859-879},
zbl = {1006.93015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p859bwm}
}
Fernández, Luis a.; Pola, Cecilia. Identification of a quasilinear parabolic equation from final data. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 859-879. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i4p859bwm/
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