Simultaneous Identification of the Parameters in the Mathematical Model of Brain Tumor Growth Dynamics Under Treatment (European Journal of Pure and Applied Mathematics, 2024)
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.
Keywords: Brain Tumor; Inverse Problem; Optimization Problem; Fréchet differentiability