Optimal control problem for cancer invasion parabolic system with nonlinear diffusion. (3rd October 2018)

• Record Type: Journal Article
• Authors: Sowndarrajan, P. T.; Shangerganesh, L.
• Is Part Of: Optimization. Volume 67:Number 10(2018)
• Page Start: 1819
• Page End: 1836
• Publication Date: 2018-10-03
• Subjects: Cancer invasion -- optimal control -- adjoint problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1486404
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we study a distributed optimal control problem of a coupled nonlinear system of reaction–diffusion equations. The system consists of three partial differential equations to represent cancer cell density, matrix-degrading enzymes concentration and oxygen concentration, and an ordinary differential equation to describe the extracellular matrix concentration. Our aim is to minimize the growth of cancer cells by controlling the production of matrix-degrading enzymes. First, we prove the existence and uniqueness of solutions of the direct problem. Then, we prove the existence of an optimal control. Finally, we derive the first-order optimality conditions and prove the existence of weak solutions of the adjoint problem.