Identification of a Quasilinear Parabolic Equation from Final Data

• Autorzy: Fernandez L. A. , Pola C.
• Języki publikacji: EN

Abstrakty

EN

We study the identification of the nonlinearities A, b and c appearing in the quasilinear parabolic equation [...] 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.

Słowa kluczowe

EN

quasilinear parabolic equation; inverse problem; parameter estimation

PL

równanie paraboliczne; problem odwrotny; estymacja parametru

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: Vol. 11, no. 4
• Strony: 859--879
• Opis fizyczny: Bibliogr. 11 poz., tab., wykr.

Twórcy

autor

Fernandez L. A.

• Dpto. Matemáticas, Estadística y Computación, Universidad de Cantabria, 39071-Santander, Spain

autor

Pola C.

• Dpto. Matemáticas, Estadística y Computación, Universidad de Cantabria, 39071-Santander, Spain

Bibliografia

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• [3] Chavent G. and Lemonnier P. (1974): Identification de la non-linéarité d'une équation parabolique quasilinéaire. - Appl. Math. Optim., Vol. 1, No. 2, pp. 121-162.
• [4] Fernández L.A. and Zuazua E. (1999): Approximate controllability for the semilinear heat equation involving gradient terms. - J. Optim. Th. Appl., Vol. 101, No. 2, pp. 307-328.
• [5] Gilbarg D. and Trudinger N.S. (1977): Elliptic Partial Differential Equations of Second Order. - Berlin: Springer.
• [6] Hanke M. and Scherzer O. (1999): Error analysis of an equation error method for the identification of the diffusion coeficient in a quasi-linear parabolic differential equation. - SIAM J. Appl. Math., Vol. 59, No. 3, pp. 1012-1027.
• [7] Kärkkäinen T. (1996): A linearization technique and error estimates for distributed parameter identification in quasilinear problems. - Numer. Funct. Anal. Optim., Vol. 17, No. 3-4, pp. 345-364.
• [8] Kunisch K. and Zou J. (1998): Iterative choices of regularization parameters in linear inverse problems. - Inverse Problems, Vol. 14, No. 5, pp. 1247-1264.
• [9] Ladyzhenskaya O.A., Solonnikov V.A. and Ural'tseva N.N. (1968): Linear and Quasilinear Equations of Parabolic Type. - Rhode Island: A.M.S.
• [10] Lions J.L. (1971): Optimal Control of Systems Governed by Partial Differential Equations. - Berlin: Springer.
• [11] Lunardi A. and Vespri V. (1991): Hölder regularity in variational parabolic non-homogeneous equations. - J. Diff. Eqns., Vol. 94, No. 1, pp. 1-40.

Uwagi

This work was partially supported by DGES (Spain), Project No. PB 98-0193.