  We investigate the evolution of tumor growth relying on a nonlinear model of
partial differential equations which incorporates mechanical laws for tissue
compression combined with rules for nutrients availability and drug
application. Rigorous analysis and simulations are presented which show the
role of nutrient and drug application in the progression of tumors. We
construct an explicit convergent numerical scheme to approximate solutions of
the nonlinear system of partial differential equations. Extensive numerical
tests show that solutions exhibit a necrotic core when the nutrient level falls
below a critical level in accordance with medical observations. The same
numerical experiment is performed in the case of drug application for the
purpose of comparison. Depending on the balance between nutrient and drug both
shrinkage and growth of tumors can occur. The role of inhomogeneous boundary
conditions, vascularization and anisotropies in the development of tumor shape
irregularities are discussed.
