A free boundary problem arising from DCIS mathematical model

被引：6

作者：

Li, Heng ^{[1
]}

Xu, Yongzhi ^{[1
]}

Zhou, Jian-Rong ^{[2
]}

机构：

[1] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[2] Foshan Univ, Dept Math, Foshan 528000, Guangdong, Peoples R China

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 10期

关键词：

nonlinear parabolic equation; free boundary problem; numerical solution; ductal carcinoma in situ (DCIS) model; CARCINOMA IN-SITU; GROWTH; TUMORS; INHIBITORS; ABSENCE;

D O I：

10.1002/mma.4246

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Ductal carcinoma in situ - a special cancer - is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright (c) 2016 John Wiley & Sons, Ltd.

引用

页码：3566 / 3579

页数：14

共 50 条

[1] A FREE-BOUNDARY PROBLEM FOR THE HEAT-EQUATION ARISING FROM A PROBLEM OF MATHEMATICAL ECONOMICS
MCKEAN, HP
[J]. IMR-INDUSTRIAL MANAGEMENT REVIEW, 1965, 6 (02): : 32 - 39
[2] Numerical algorithms for a free boundary problem model of DCIS and a related inverse problem
Liu Keji
Xu Yongzhi
Xu Dinghua
[J]. APPLICABLE ANALYSIS, 2020, 99 (07) : 1181 - 1194
[3] A free boundary problem arising in a model of wound healing
Chen, XF
Friedman, A
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 32 (04) : 778 - 800
[4] Another way of solving a free boundary problem related to DCIS model
Zhou, Jianrong
Xu, Yongzhi
Li, Heng
[J]. APPLICABLE ANALYSIS, 2021, 100 (15) : 3244 - 3258
[5] Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model
Avner Friedman
Bei Hu
[J]. Archive for Rational Mechanics and Analysis, 2006, 180 : 293 - 330
[6] Bifurcation from stability to instability for a free boundary problem arising in a tumor model
Friedman, A
Hu, B
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2006, 180 (02) : 293 - 330
[7] On a free boundary problem arising from population biology
Dancer, EN
Du, YH
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2003, 52 (01) : 51 - 67
[8] Asymptotic stability for a free boundary problem arising in a tumor model
Friedman, Avner
Hu, Bei
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 227 (02) : 598 - 639
[9] A PARABOLIC FREE BOUNDARY PROBLEM ARISING IN A MODEL OF CELL POLARIZATION
Logioti, A.
Niethammer, B.
Roeger, M.
Velazquez, J. J. L.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (01) : 1214 - 1238
[10] A free boundary problem arising from pricing convertible bond
Yang, Zhou
Yi, Fahuai
[J]. APPLICABLE ANALYSIS, 2010, 89 (03) : 307 - 323

← 1 2 3 4 5 →