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We investigate the evolution of tumor growth relying on a nonlinear model ofpartial differential equations which incorporates mechanical laws for tissuecompression combined with rules for nutrients availability and drugapplication. Rigorous analysis and simulations are presented which show therole of nutrient and drug application in the progression of tumors. Weconstruct an explicit convergent numerical scheme to approximate solutions ofthe nonlinear system of partial differential equations. Extensive numericaltests show that solutions exhibit a necrotic core when the nutrient level fallsbelow a critical level in accordance with medical observations. The samenumerical experiment is performed in the case of drug application for thepurpose of comparison. Depending on the balance between nutrient and drug bothshrinkage and growth of tumors can occur. The role of inhomogeneous boundaryconditions, vascularization and anisotropies in the development of tumor shapeirregularities are discussed.

Analysis and Simulation on a Model for the Evolution of Tumors under the Influence of Nutrient and Drug Application