Mathematical analysis of a model of tumour invasion and simulations

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume4
Issue number3
Publication statusPublished - 30-11-2010

Fingerprint

Invasion
Mathematical Analysis
Tumors
Tumor
Asymptotic Profile
Angiogenesis
A Priori Estimates
System Modeling
Global Existence
Evolution Equation
Solvability
Simulation
Computer Simulation
Mathematical Model
Mathematical models
Computer simulation
Arbitrary
Model

All Science Journal Classification (ASJC) codes

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

Cite this

@article{5293db95cc9b49ac91ae0ced4c546f26,
title = "Mathematical analysis of a model of tumour invasion and simulations",
abstract = "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.",
author = "Akisato Kubo",
year = "2010",
month = "11",
day = "30",
language = "English",
volume = "4",
pages = "187--194",
journal = "International Journal of Mathematical Models and Methods in Applied Sciences",
issn = "1998-0140",
publisher = "North Atlantic University Union NAUN",
number = "3",

}

TY - JOUR

T1 - Mathematical analysis of a model of tumour invasion and simulations

AU - Kubo, Akisato

PY - 2010/11/30

Y1 - 2010/11/30

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78649342150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649342150&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:78649342150

VL - 4

SP - 187

EP - 194

JO - International Journal of Mathematical Models and Methods in Applied Sciences

JF - International Journal of Mathematical Models and Methods in Applied Sciences

SN - 1998-0140

IS - 3

ER -