Kubo, A., Saito, N., Suzuki, T. and Hoshino, H. (2006) Mathematical Models of Tumour Angiogenesis and Simulations, Theory of Bio-Mathematics and Its Application. RIMS Kokyuroku, 1499, 135-146.

has been cited by the following article:

• TITLE: Nonlinear Evolution Equations and Its Application to a Tumour Invasion Model

  AUTHORS: Akisato Kubo, Yuto Miyata, Hidetoshi Kobayashi, Hiroki Hoshino, Naoki Hayashi

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

  JOURNAL NAME: Advances in Pure Mathematics, Vol.6 No.12, November 17, 2016

  ABSTRACT: 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.