# 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

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topFernández, 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 -

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