Simultaneous Identification of the Parameters in the Mathematical Model of Brain Tumor Growth Dynamics Under Treatment

Authors

  • Salih Tatar Alfaisal University
  • Mohamed BenSalah
  • Maryam Alamil

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5386

Keywords:

Brain Tumor, Inverse Problem, Optimization Problem, Fréchet differentiability

Abstract

This paper is devoted to an inverse problem for a nonlinear parabolic equation related to brain tumor dynamics. After reformulating the inverse problem as a minimization problem, we prove the existence and stability of the solution to the minimization problem. Based on the Fréchet differentiability of the objective (cost) functional,  we develop an efficient iterative procedure  for the numerical solution to the minimization problem. Numerical examples with noise-free and noisy data illustrate applicability and accuracy of the proposed method to some extent.

Author Biographies

  • Salih Tatar, Alfaisal University

    College of Science and General Studies, Alfaisal University, Riyadh 11533, Saudi Arabia

  • Mohamed BenSalah

    Department of Computer Sciences, Higher Institute of Applied Science and Technology of Sousse, University of Sousse, Rue Tahar Ben Achour, Sousse 4003, Tunisia

  • Maryam Alamil

    College of Science and General Studies, Alfaisal University, Riyadh 11533, Saudi Arabia

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 Salih Tatar, Mohamed BenSalah, Maryam Alamil

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How to Cite

Simultaneous Identification of the Parameters in the Mathematical Model of Brain Tumor Growth Dynamics Under Treatment. (2024). European Journal of Pure and Applied Mathematics, 17(4), 2651-2675. https://doi.org/10.29020/nybg.ejpam.v17i4.5386