Paper Info
Title
Numerical Solution Of Optimal Control Problem For A Model Of Tumour Growth With Drug Application
Abstract
In this study, a combination of spectral and fixed point methods is used to solve an optimal control problem for a model of tumour growth. The growth of tumour is modelled using three first-order hyperbolic equations describing the evolution of cells and two second-order parabolic equations describing the diffusion of nutrient and drug concentration. In the optimal control problem, four control variables are employed to control the concentration of nutrient and drug on the boundary and inside the tumour. Since the problem is nonlinear, applying the fixed point method, in each step of iteration, the problem is changed to a linear one and the parabolic equations are solved using the spectral method. The convergence and stability of method are proven. Some examples are considered to illustrate the efficiency of method. Finally, some figures are provided to reflect the effects of control on the densities of tumourcells.
Year
DOI
Venue
2019
10.1080/00207179.2018.1458159
INTERNATIONAL JOURNAL OF CONTROL
Keywords
DocType
Volume
Optimal control, parabolic-hyperbolic equation, free boundary problem, spectral method, fixed point method
Journal
92
Issue
ISSN
Citations 
11
0020-7179
0
PageRank 
References 
Authors
0.34
1
2
Name
Order
Citations
PageRank
Sakine Esmaili121.74
M. R. Eslahchi28813.65