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Asymptotic Behavior of a Tumor Angiogenesis Model with Haptotaxis

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chi Xu & Yifu Wang, 2020. "Asymptotic Behavior of a Tumor Angiogenesis Model with Haptotaxis," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:664-:d:351210
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