21 Citations (Scopus)

Abstract

© 2014 I. V. Zhukova, E. P. Kolpak and Yu. E. Balykina. The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.
Original languageEnglish
Pages (from-to)1455-1466
JournalApplied Mathematical Sciences
Issue number30
DOIs
Publication statusPublished - 2014

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Tumors
Tumor
Mathematical Model
Mathematical models
Cell
Differential equations
Cells
Derivatives
Partial derivative
System of Differential Equations
Straight Line
Evaluation

Cite this

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title = "Mathematical model of growing tumor",
abstract = "{\circledC} 2014 I. V. Zhukova, E. P. Kolpak and Yu. E. Balykina. The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.",
author = "I.V. Zhukova and E.P. Kolpak and Y.E. Balykina",
year = "2014",
doi = "10.12988/ams.2014.4135",
language = "English",
pages = "1455--1466",
journal = "Applied Mathematical Sciences",
issn = "1312-885X",
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Mathematical model of growing tumor. / Zhukova, I.V.; Kolpak, E.P.; Balykina, Y.E.

In: Applied Mathematical Sciences, No. 30, 2014, p. 1455-1466.

Research output

TY - JOUR

T1 - Mathematical model of growing tumor

AU - Zhukova, I.V.

AU - Kolpak, E.P.

AU - Balykina, Y.E.

PY - 2014

Y1 - 2014

N2 - © 2014 I. V. Zhukova, E. P. Kolpak and Yu. E. Balykina. The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.

AB - © 2014 I. V. Zhukova, E. P. Kolpak and Yu. E. Balykina. The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.

U2 - 10.12988/ams.2014.4135

DO - 10.12988/ams.2014.4135

M3 - Article

SP - 1455

EP - 1466

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1312-885X

IS - 30

ER -