Asymptotic Behavior of a Tumor Angiogenesis Model with Haptotaxis

Chi Xu and Yifu Wang
Additional contact information
Chi Xu: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Yifu Wang: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2020, vol. 8, issue 5, 1-21

Abstract: This paper considers the existence and asymptotic behavior of solutions to the angiogenesis system p t = Δ p − ρ ∇ · ( p ∇ w ) + λ p ( 1 − p ) , w t = − γ p w β in a bounded smooth domain Ω ⊂ R N ( N = 1 , 2 ) , where ρ , λ , γ > 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; haptotaxis; asymptotic behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/5/664/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/5/664/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:5:p:664-:d:351210

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().