| In vivo tumor growth is a complicated phenomenon which involves several interrelated processes, it has the regulating mechanism in the complex, multiple input, multiple output, etc. The growth of tumor cells is different from normal cells mainly is that they can continue to grow. The normal update group the number of cell proliferation and death in roughly equ-al, in a state of dynamic balance; And tumor cell proliferation and death in the organization, and is often the former than the latter. Therefore. If there are no restrictions, tumor cells can rapid growth to a considerable number (group volume in general). But the truth is, when the number of tumor cells increase to some degree, due to the supply of nutrients can not me-et the needs of tumor cells, so as to make the growth slowing in the rate of tumor cells.The growth and development of solid tumor occurs in two distinct phases:the avascufar and the vascular phase. During the former growth phase the tumour remains in a diffusion-limited dormant state of a few millimeters in diameter,while during the later phase.invasion and metastasis do take place. In this paper we study a mathematical model of cancer cell break out and invasion of normal tissue or extracellular matrix. Using the theory of mathematical strictly analyzes the existence and uniqueness of global solution. The whole paper consists of two chapters.In the first chapter, we give an introduction, this part mainly has four sections, respectively is introduced:the source of the subject, research significance, research status at home and abroad and some useful symbols and the fundamental lemmas.In chapter2, the model consists of a system of four Reaction-diffusion-taxis partial differential equations and a degenerate parabolic partial differential equations. By using the parabolic Lp-theory, the parabolic Schauder estimates, principle of comparison and the Banach fixed point theorem, we prove that this system has a unique global solution. |
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