Author(s)

Akisato Kubo¹, Yuto Miyata², Hidetoshi Kobayashi³, Hiroki Hoshino¹, Naoki Hayashi⁴

¹Department of Mathematics, School of Health Sciences, Fujita Health University, Toyoake, Japan.
²Medical Radiation Sciences, Graduate School of Health Sciences, Fujita Health University, Toyoake, Japan.
³Department of Radiation Oncology, School of Medicine, Fujita Health University, Toyoake, Japan.
⁴Faculty of Radiological Technology, School of Health Sciences, Fujita Health University, Toyoake, Japan.

We consider nonlinear evolution equations with logistic term satisfying initial Neumann-boundary condition and show global existence in time of solutions to the problem in arbitrary space dimension by using the method of energy. Applying the result to a mathematical model of tumour invasion, we discuss the property of the rigorous solution to the model. Finally we will show the time depending relationship and interaction between tumour cells, the surrounding tissue and matrix degradation enzymes in the model by computer simulations. It is seen that our mathematical result of the existence and asymptotic behaviour of solutions verifies our simulations, which also confirm the mathematical result visibly.

Nonlinear Evolution Equation, Mathematical Analysis, Tumour Invasion, Proliferation, Re-Establishment

Kubo, A. , Miyata, Y. , Kobayashi, H. , Hoshino, H. and Hayashi, N. (2016) Nonlinear Evolution Equations and Its Application to a Tumour Invasion Model. Advances in Pure Mathematics, 6, 878-893. doi: 10.4236/apm.2016.612066.