Identification of source term in a nonlinear degenerate parabolic equation with memory

Soufiane Abid; Khalid Atifi; El-Hassan Essoufi; Abderrahim Zafrar

Applications of Mathematics (2024)

  • Issue: 2, page 209-232
  • ISSN: 0862-7940

Abstract

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In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.

How to cite

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Abid, Soufiane, et al. "Identification of source term in a nonlinear degenerate parabolic equation with memory." Applications of Mathematics (2024): 209-232. <http://eudml.org/doc/299259>.

@article{Abid2024,
abstract = {In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.},
author = {Abid, Soufiane, Atifi, Khalid, Essoufi, El-Hassan, Zafrar, Abderrahim},
journal = {Applications of Mathematics},
keywords = {inverse source problem; nonlinear parabolic equation; memory term; optimal control},
language = {eng},
number = {2},
pages = {209-232},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Identification of source term in a nonlinear degenerate parabolic equation with memory},
url = {http://eudml.org/doc/299259},
year = {2024},
}

TY - JOUR
AU - Abid, Soufiane
AU - Atifi, Khalid
AU - Essoufi, El-Hassan
AU - Zafrar, Abderrahim
TI - Identification of source term in a nonlinear degenerate parabolic equation with memory
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 209
EP - 232
AB - In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers' type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.
LA - eng
KW - inverse source problem; nonlinear parabolic equation; memory term; optimal control
UR - http://eudml.org/doc/299259
ER -

References

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