Modelling and numerical analysis of complex tumour models

Avascular tumour growth is the initial stage of cancer development, wherein the tumour tissue is devoid of any blood vessels. This thesis develops mathematical models of several variants of avascular tumour growth, such as in living tissues or in a controlled laboratory setting; designs numerical schemes; and conducts rigorous mathematical analysis. Many classical difficulties associated with the mathematical study of tumour growth, such as the time-dependent boundary and computationally expensive numerical schemes, are addressed in this thesis. Along with this, several mathematical results are also derived that have applications in related problems.