## Mathematical Analysis of Non-Local Tumour Invasion Model and Simulations

 AUTHOR(S): Akisato Kubo, Yuto Miyata TITLE Mathematical Analysis of Non-Local Tumour Invasion Model and Simulations PDF 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. 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(2018) Mathematical Analysis of Non-Local Tumour Invasion Model and Simulations. International Journal of Mathematical and Computational Methods, 3, 9-15 Copyright © 2018 Author(s) retain the copyright of this article.This article is published under the terms of the Creative Commons Attribution License 4.0