In this paper we investigate a mathematical model of non-local tumour invasion with proliferation proposed by Gerisch and Chaplain. We show the global existence in time and asymptotic profile of the solution to the initial boundary value problem for the model. For this purpose we deal with the problem applying the argument of the singular integral operator to the non-local term, and we finally arrive at our desired result. In order to show computer simulations of the model we consider an approximation problem of the model, and we can discuss the time dependent change of the non-local tumour invasion process by computer simulations.
Non-local model, mathematical analysis, tumour invasion, Taylor expansion, simulation, integral operator
Cite this paper
Akisato Kubo, Yuto Miyata. (2019) Characterization of an Integral Operator Arised in Non-Local Tumour Invasion Model and its Mathematical Analysis. International Journal of Mathematical and Computational Methods, 4, 10-16
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