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  3. وجود و یکتایی جواب برای دو مدل ریاضی با مرز آزاد برای یک غده کروی
وجود و یکتایی جواب برای دو مدل ریاضی با مرز آزاد برای یک غده کروی
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وجود و یکتایی جواب برای دو مدل ریاضی با مرز آزاد برای یک غده کروی

اسمعیلی، سکینه Esmaili, Sakine

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

Esmaili, Sakine | 2010

945 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

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