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

Maciej Cytowski, Akio Ito, and Marek Niezgódka. "Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model." Banach Center Publications 86.1 (2009): 45-58. <http://eudml.org/doc/281896>.

@article{MaciejCytowski2009,
abstract = {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.},
author = {Maciej Cytowski, Akio Ito, Marek Niezgódka},
journal = {Banach Center Publications},
keywords = {tumor invasion model; uniqueness and existence of solutions},
language = {eng},
number = {1},
pages = {45-58},
title = {Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model},
url = {http://eudml.org/doc/281896},
volume = {86},
year = {2009},
}

TY - JOUR
AU - Maciej Cytowski
AU - Akio Ito
AU - Marek Niezgódka
TI - Uniqueness and local existence of solutions to an approximate system of a 1D simplified tumor invasion model
JO - Banach Center Publications
PY - 2009
VL - 86
IS - 1
SP - 45
EP - 58
AB - 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.
LA - eng
KW - tumor invasion model; uniqueness and existence of solutions
UR - http://eudml.org/doc/281896
ER -