Identification of a quasilinear parabolic equation from final data

Luis a. Fernández; Cecilia Pola

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 4, page 859-879
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Fernández, Luis a., and Pola, Cecilia. "Identification of a quasilinear parabolic equation from final data." International Journal of Applied Mathematics and Computer Science 11.4 (2001): 859-879. <http://eudml.org/doc/207535>.

@article{Fernández2001,
abstract = {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.},
author = {Fernández, Luis a., Pola, Cecilia},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {quasilinear parabolic equation; inverse problem; parameter estimation; identification},
language = {eng},
number = {4},
pages = {859-879},
title = {Identification of a quasilinear parabolic equation from final data},
url = {http://eudml.org/doc/207535},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Fernández, Luis a.
AU - Pola, Cecilia
TI - Identification of a quasilinear parabolic equation from final data
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 4
SP - 859
EP - 879
AB - 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.
LA - eng
KW - quasilinear parabolic equation; inverse problem; parameter estimation; identification
UR - http://eudml.org/doc/207535
ER -

References

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  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. Zbl0917.65053
  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. 
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