Loading...

Existence and Uniqueness of Solution for Two Free Boundary Problems Modelling Tumor Growth

Esmaili, Sakine | 2010

578 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41156 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaaraki, Mahmoud
  7. Abstract:
  8. This thesis is based on articles [18,15]. Zhao [18] has studied a free boundary problem modeling the growth of tumors with drug application. In this model live cells are two kindes: proliferative cells and quiescent cells. This model consists of two nonlinear second-order parabolic equations describing the diffusion of nutrient and drug concentration, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells. He has proved that this free boundary problem has a unique global solution. Tao and Chen [15] have studied another free boundary problem modelling the growth of an avascular tumour with drug application. The tumour consists of two cell populations: live cells and dead cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations. The tumour surface is a moving boundary, which satisfies an integro-differential equation. The nutrient concentration and the drug concentration satisfy nonlinear diffusion equations. They have proved that this free boundary problem has a unique global solution. Furthermore, they investigated the combined effects of a drug and a nutrient on an avascular tumour growth. They proved that the tumour shrinks to a necrotic core with radius Rs > 0 and that the global solution converges to a trivial steady-state solution under some natural assumptions on the model parameters. They also proved that an untreated tumour shrinks to a dead core or continually grows to an infinite size, which depends on the different parameter conditions
  9. Keywords:
  10. Tumor Growth ; Global Solution ; Parabolic-Hyperbolic Equation ; Elliptic-Hyperbolic Equation ; Free Boundry Problem

 Digital Object List

 Bookmark

No TOC