Mathematical analysis of a model of tumour invasion and simulations

Akisato Kubo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study a parabolic ODE system modeling tumour invasion proposed by Anderson and Chaplain in 2003. Then we will apply the approach used in mathematical models of tumour angiogenesis to it and show the solvability and the asymptotic profile of the solution of it. Actually in use of the transformation of Levine and Sleeman, we reduce it to a system consist of evolution equations. Then, we show global existence in time of the solution in arbitrary space dimension by a priori estimate. Finally we show some results of computer simulations of the model with the help of our mathematical analysis.

Original languageEnglish
Pages (from-to)187-194
Number of pages8
JournalInternational Journal of Mathematical Models and Methods in Applied Sciences
Issue number3
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Mathematical Physics
  • Computational Mathematics
  • Applied Mathematics


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