Mathematical model of cancer with radiotherapy and chemotherapy treatments

Abstract

The typical treatment for tumor involves a combination of radiation therapy and chemotherapy. In this study, we explore a mathematical model based on proliferation and diffusion, considering the impacts of both radiotherapeutic and chemotherapeutic treatments. The mathematical model is formulated as a system of partial differential equations, accompanied by initial, boundary, and free boundary conditions. Existence and uniqueness of this mathematical problem are obtained by developing an iteration algorithm in this paper.

Keywords:

• Nonlinear parabolic equation
• free boundary problem

2010 Mathematics Subject Classifications:

• 35K15
• 35K20
• 35R35
• 35Q68

Acknowledgments

The author dedicates this work to Dr Yongzhi Xu on the occasion of his 70th birthday, expressing profound gratitude and sincere thanks for his invaluable guidance.

Disclosure statement

No potential conflict of interest was reported by the author(s).