Mathematical modelling; analysis and numerical simulations for cancer cell

In this thesis, a model considering one of the most important stages of metastasis, namely the tissue invasion is investigated by focusing on the role of the matrix degrading enzymes, chemotaxis and haptotaxis. Furthermore, the existence of a unique weak solution for the corresponding model is proved by using an iterative procedure. Next the model is solved numerically by using finite difference method. It has been seen that the results of the numerical simulations agree well with the expected behaviour of the invasion. Moreover the effect of the factors such as chemo-taxis, haptotaxis and re-establishment of cancer cells and the tissue, on invasion, is examined by the help of the numerical simulations.