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1 International Journal of Applied Mathematics and Computer Science

1 2001

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Identification of a Quasilinear Parabolic Equation from Final Data

Fernandez L. A., Pola C.

International Journal of Applied Mathematics and Computer Science

2001

Vol. 11, no 4

859-879

We study the identification of the nonlinearities A, vec{b} and c appearing in the quasilinear parabolic equation y_t - div (A(y) nabla y + vec{b} (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, vec{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.