Mathematical Analysis of Non-Local Tumour Invasion Model and Simulations

Abstract: In this paper we investigate a mathematical model of non-local tumour invasion with proliferation proposed by Grisch and Chaplain in 2008. For the better understanding of the model we consider an approximation model expanding the non-local term into Taylor series. We prove the global existence in time and asymptotic profile of the solution to the initial boundary value problem for the approximation model in 1 spacial dimension. Applying known mathematical results of usual(local) tumour invasion models, which are corresponding to the same type problem of Chaplain and Lolas model, we discuss the existence and property of solutions to the problem. Finally we show the time dependent change of the non-local tumour invasion process by computational simulations of the approximation model.