Fisher type waves in a model of invasive tumor growth

A mathematical model for the invasive tumor growth which includes nutrient distribution in tissue is developed. This model adequately describes constant rate of the tumor linear size growth with time and the formation of necrotic region in the tumor interior, observed in experiments. The existence of autowave solutions is demonstrated and their properties are investigated. The results are compared with the properties of the Kolmogorov–Petrovskii–Piskunov and Fisher equations. The perspective of further investigation and development of the model for studying glioma is discussed.