Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy

Yifu Wang*, Chi Xu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

This paper deals with an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy ut = u - (uv) + μu(1 - u) - uz,vt = -(u + w)v,wt = w - (wv) - w + uz,zt = Dzz - z - uz + βw, in a smoothly bounded domain ω 3 with β > 0, μ > 0 and Dz > 0. Based on a self-map argument, it is shown that under the assumption βmax{1,u0L∞(ω)} < 1 + (1 +1 minx ωu0(x))-1, this problem possesses a uniquely determined global classical solution (u,v,w,z) for certain type of small data (u0,v0,w0,z0). Moreover, (u,v,w,z) is globally bounded and exponentially stabilizes toward its spatially homogeneous equilibrium (1, 0, 0, 0) as t →∞.

Original languageEnglish
Pages (from-to)2313-2335
Number of pages23
JournalMathematical Models and Methods in Applied Sciences
Volume33
Issue number11
DOIs
Publication statusPublished - 1 Oct 2023

Keywords

  • Haptotaxis
  • asymptotic behavior
  • boundedness
  • oncolytic virotherapy

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