Asymptotic behavior of a tumor angiogenesis model with haptotaxis

Chi Xu; Yifu Wang

doi:10.3390/MATH8050664

Asymptotic behavior of a tumor angiogenesis model with haptotaxis

Chi Xu^*, Yifu Wang

^*此作品的通讯作者

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system p_t = Δp - ρ∇ (p∇w) + λp(1-p), w_t =-ypw^β in a bounded smooth domain Ω ⊂ R^N(N = 1, 2), where p, λ, y > 0 and β ≥ 1. More precisely, it is shown that the corresponding solution (p, w) converges to (1, 0) with an explicit exponential rate if β = 1, and polynomial rate if β > 1 as t → ∞, respectively, in L∞-norm.

源语言	英语
文章编号	664
期刊	Mathematics
卷	8
期	5
DOI	https://doi.org/10.3390/MATH8050664
出版状态	已出版 - 1 5月 2020

访问文件

10.3390/MATH8050664

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{7e607cb5fb6944b8b5e9916b781b8f97,

title = "Asymptotic behavior of a tumor angiogenesis model with haptotaxis",

abstract = "This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system pt = Δp - ρ∇ (p∇w) + λp(1-p), wt =-ypwβ in a bounded smooth domain Ω ⊂ RN(N = 1, 2), where p, λ, y > 0 and β ≥ 1. More precisely, it is shown that the corresponding solution (p, w) converges to (1, 0) with an explicit exponential rate if β = 1, and polynomial rate if β > 1 as t → ∞, respectively, in L∞-norm.",

keywords = "Angiogenesis, Asymptotic behavior, Haptotaxis",

author = "Chi Xu and Yifu Wang",

note = "Publisher Copyright: {\textcopyright} 2020 by the authors.",

year = "2020",

month = may,

day = "1",

doi = "10.3390/MATH8050664",

language = "English",

volume = "8",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "5",

}

TY - JOUR

T1 - Asymptotic behavior of a tumor angiogenesis model with haptotaxis

AU - Xu, Chi

AU - Wang, Yifu

PY - 2020/5/1

Y1 - 2020/5/1

N2 - This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system pt = Δp - ρ∇ (p∇w) + λp(1-p), wt =-ypwβ in a bounded smooth domain Ω ⊂ RN(N = 1, 2), where p, λ, y > 0 and β ≥ 1. More precisely, it is shown that the corresponding solution (p, w) converges to (1, 0) with an explicit exponential rate if β = 1, and polynomial rate if β > 1 as t → ∞, respectively, in L∞-norm.

AB - This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system pt = Δp - ρ∇ (p∇w) + λp(1-p), wt =-ypwβ in a bounded smooth domain Ω ⊂ RN(N = 1, 2), where p, λ, y > 0 and β ≥ 1. More precisely, it is shown that the corresponding solution (p, w) converges to (1, 0) with an explicit exponential rate if β = 1, and polynomial rate if β > 1 as t → ∞, respectively, in L∞-norm.

KW - Angiogenesis

KW - Asymptotic behavior

KW - Haptotaxis

UR - http://www.scopus.com/inward/record.url?scp=85085573654&partnerID=8YFLogxK

U2 - 10.3390/MATH8050664

DO - 10.3390/MATH8050664

M3 - Article

AN - SCOPUS:85085573654

SN - 2227-7390

VL - 8

JO - Mathematics

JF - Mathematics

IS - 5

M1 - 664

ER -

Asymptotic behavior of a tumor angiogenesis model with haptotaxis

摘要

访问文件

其它文件与链接

指纹

引用此