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

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	664
Journal	Mathematics
Volume	8
Issue number	5
DOIs	https://doi.org/10.3390/MATH8050664
Publication status	Published - 1 May 2020

Keywords

Angiogenesis
Asymptotic behavior
Haptotaxis

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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",

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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

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VL - 8

JO - Mathematics

JF - Mathematics

IS - 5

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ER -

Asymptotic behavior of a tumor angiogenesis model with haptotaxis

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