Existence of Global Solution for Two Models of Cancer Invasion

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Torabi, Mousa | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42444 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis we investigating two models of cancer invasion .First, a general mathematical model of cancer invasion is presented. In this model there are three factors: tumor cell, extracellular matrix and enzyme. The model consists of a parabolic partial differential equation (PDE) describing the evolution of tumor cell density , an ordinary differential equation modeling of extracellular matrix and a parabolic PDE governing the evolution of the matrix degrading enzyme concentration. This model is investigated in two special versions for existence and uniqueness of global solutions. In the first model we neglect the remodeling term, this model is named the chemotaxis-haptotaxis model. Under a restrictive assumption on the coefficients, the global existence and uniqueness of solutions is proved. In the second model the chemotaxis term is omitted, this model is named the haptotaxis model. In this model, under a restrictive assumption on the coefficients, the global existence and uniqueness of solutions is proved by establishing some delicate a priori estimates
Keywords:
Apriori Estimate ; Global Solution ; Parabolic Equations ; Parabolic Differential Equations ; Cancer Invasion Model

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