Geodesic
Identification of a Quasilinear Parabolic Equation from Final Data
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 4, pp. 859-879.

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We study the identification of the nonlinearities A, vecb and c appearing in the quasilinear parabolic equation y_t - div (A(y) nabla y + vecb (y)) + c(y) = u in Omega x (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 Omega, for each source term u. Our work can be divided into two parts. Firstly, the uniqueness of A, vecb 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.
Keywords: quasilinear parabolic equation, inverse problem, parameter estimation
Mots-clés : quasi-liniowy, zagadnienie odwrotności, oznaczenie parametru 
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     author = {Fernandez, L. A. and Pola, C.},
     title = {Identification of a {Quasilinear} {Parabolic} {Equation} from {Final} {Data}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {859--879},
     publisher = {mathdoc},
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     number = {4},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_4_a5/}
}
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Fernandez, L. A.; Pola, C. Identification of a Quasilinear Parabolic Equation from Final Data. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 4, pp. 859-879. http://geodesic.mathdoc.fr/item/IJAMCS_2001_11_4_a5/