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Identification of a quasilinear parabolic equation from final data

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Fernández L. A., Pola C.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 4

859-879

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.

Ograniczanie wyników

1 International Journal of Applied Mathematics and Computer Science

1 Fernández L. A.

1 Pola C.

1 2001

Wyniki wyszukiwania

Identification of a quasilinear parabolic equation from final data