Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model

• Autorzy: Maciej Cytowski , Akio Ito , Marek Niezgódka
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we consider an approximate system of one-dimensional simplified tumor invasion model, which was originally proposed by Chaplain and Anderson in [chaplain-anderson-03]. The simplified tumor invasion model is composed of PDE and ODE. Actually, the PDE is the balance equation of the density of tumor cells and the ODE describes the dynamics of concentration of extracellular matrix. In this model, we take into account that the random motility of the density of tumor cells is given by a function of space and time, that is, it is not a positive constant. Moreover, the PDE contains a (nonlinear) function which describes the proliferation as well as the apoptosis of tumor cells. Our main objective is to give the local existence and uniqueness of the solutions to the approximate system.

Kategorie tematyczne

• 35M99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 45-58

Daty

wydano

2009

Twórcy

autor

Maciej Cytowski

• Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, Pawińskiego 5a, 02-106 Warszawa, Poland

autor

Akio Ito

• Department of Electronic Engineering and Computer Science, School of Engineering, Kinki University, 1 Takayaumenobe, Higashihiroshimashi, Hiroshima, 739-2116, Japan

autor

Marek Niezgódka

• Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, Pawińskiego 5a, 02-106 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc86-0-3