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2001 | 11 | 4 | 859-879
Tytuł artykułu

Identification of a quasilinear parabolic equation from final data

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
11
Numer
4
Strony
859-879
Opis fizyczny
Daty
wydano
2001
otrzymano
2001-06-01
poprawiono
2001-09-01
Twórcy
  • Dpto. Matematicas, Estadistica y Computacion, Universidad de Cantabria, 39071-Santander, Spain
autor
  • Dpto. Matematicas, Estadistica y Computacion, Universidad de Cantabria, 39071-Santander, Spain
Bibliografia
  • Banks H.T. and Kunisch K. (1989): Estimation Techniques for Distributed Parameter Systems. - Boston: Birkhauser.
  • Barbu V. and Kunisch K. (1995): Identification of nonlinear parabolic equations. - Contr. Theory Adv. Tech., Vol.10, No.4, pp.1959-1980.
  • Chavent G. and Lemonnier P. (1974): Identification de la non-linéarite d'une équation parabolique quasilinéaire. - Appl. Math. Optim., Vol.1, No.2, pp.121-162.
  • 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.
  • Gilbarg D. and Trudinger N.S. (1977): Elliptic Partial Differential Equations of Second Order. - Berlin: Springer.
  • Hanke M. and Scherzer O. (1999): Error analysis of an equation error method for the identification of the diffusion coefficientin a quasi-linear parabolic differential equation. - SIAM J.Appl. Math., Vol.59, No.3, pp.1012-1027.
  • 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.
  • Kunisch K. and Zou J. (1998): Iterative choices of regularization parameters in linear inverse problems. - Inverse Problems, Vol.14, No.5, pp.1247-1264.
  • Ladyzhenskaya O.A., Solonnikov V.A. and Ural'tseva N.N.(1968): Linear and Quasilinear Equations of Parabolic Type.- Rhode Island: A.M.S.
  • Lions J.L. (1971): Optimal Control of Systems Governed by Partial Differential Equations. - Berlin: Springer.
  • Lunardi A. and Vespri V. (1991): Holder regularity invariational parabolic non-homogeneous equations. - J. Diff. Eqns., Vol.94, No.1, pp.1-40.
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Bibliografia
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