Long time behavior of a model for the evolution of morphogens in a growing tissue

被引：5

作者：

Coclite, G. M. ^{[1
]}

Coclite, M. M. ^{[2
]}

机构：

[1] Polytech Univ Bari, Dept Mech Math & Management, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari, Italy

来源：

PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2020年 / 1卷 / 01期

关键词：

Singular diffusion; Neumann boundary conditions; Long time behavior; Morphogen evolution; SIZE; PROLIFERATION; PATTERN; GROWTH;

D O I：

10.1007/s42985-019-0007-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The long time behavior of a model for the regulation of growth and patterning in developing tissues by diffusing morphogens is analyzed. Such model is expressed in terms of a system of nonlinear PDEs. The key tool in the analysis is the transformation of such system to an equation with singular diffusion.

引用

页数：39

共 22 条

[1] Model for the regulation of size in the wing imaginal disc of Drosophila
Aegerter-Wilmsen, Tinri
Aegerter, Christof M.
Hafen, Ernst
Basler, Konrad
[J]. MECHANISMS OF DEVELOPMENT, 2007, 124 (04) : 318 - 326
[2] The Decapentaplegic morphogen gradient: from pattern formation to growth regulation
Affolter, Markus
Basler, Konrad
[J]. NATURE REVIEWS GENETICS, 2007, 8 (09) : 663 - 674
[3] LARGE TIME BEHAVIOR OF SOLUTIONS OF THE POROUS-MEDIUM EQUATION IN BOUNDED DOMAINS
ARONSON, DG
PELETIER, LA
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1981, 39 (03) : 378 - 412
[4] ARONSON DG, 1979, CR ACAD SCI A MATH, V288, P103
[5] Scaling morphogen gradients during tissue growth by a cell division rule
Averbukh, Inna
Ben-Zvi, Danny
Mishra, Siddhartha
Barkai, Naama
[J]. DEVELOPMENT, 2014, 141 (10): : 2150 - 2156
[6] Coclite GM, 2017, Z ANGEW MATH PHYS, V68, DOI 10.1007/s00033-017-0838-0
[7] On a model for the evolution of morphogens in growing tissue III: θ < log(2)
Coclite, G. M.
Coclite, M. M.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 263 (02) : 1079 - 1124
[8] ON A MODEL FOR THE EVOLUTION OF MORPHOGENS IN A GROWING TISSUE
Coclite, G. M.
Coclite, M. M.
Mishra, S.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (03) : 1575 - 1615
[9] On nonlinear parabolic equations of very fast diffusion
Daskalopoulos, P
delPino, M
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 137 (04) : 363 - 380
[10] Day SJ, 2000, DEVELOPMENT, V127, P2977

← 1 2 3 →