The existence of solutions for tumor invasion models with time and space dependent diffusion

Risei Kano

doi:10.3934/dcdss.2014.7.63

Article Contents

2014, Volume 7, Issue 1: 63-74. Doi: 10.3934/dcdss.2014.7.63

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The existence of solutions for tumor invasion models with time and space dependent diffusion

Risei Kano^1,

1.
Department of Mathematics, Faculty of Education, Kochi University, Akebonotyo 2-5-1, Kochi, Kochi, 780-8019

Received: March 2012

Revised: May 2012

Published: February 2014

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Abstract

We shall show the existence of a solution for a nonlinear parabolic system. This system is a tumor invasion model which has the time and space dependent diffusion coefficient. In this paper, we apply an existence result for Quasi-Variational Inequalities. Quasi-Variational Inequality is a problem to find a function which satisfies a variational inequality in which the constraint depends upon the unknown function. In this paper, I shall show how to approach to our tumor invasion model by Quasi-Variational inequality, and obtain a solution for it.

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Mathematics Subject Classification: Primary: 35K45; Secondary: 35K50.

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References

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