A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy. (September 2020)

• Record Type: Journal Article
• Authors: Tao, Youshan; Winkler, Michael
• Is Part Of: Nonlinear analysis. Volume 198(2020)
• Publication Date: 2020-09
• Subjects: 35B33 -- 35B40 -- 35K57 -- 35Q92 -- 92C17; Haptotaxis -- Critical parameter -- Boundedness; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111870
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In a two-dimensional smoothly bounded domain, we consider the oncolytic virotherapy model given by u t = Δ u − ∇ ⋅ ( u ∇ v ) − ρ u z, v t = − ( u + w ) v, w t = D w Δ w − w + u z, z t = D z Δ z − z − u z + β w, with parameters D w > 0, D z > 0, β > 0 and ρ ≥ 0 . According to previous findings, a corresponding Neumann initial–boundary value problem possesses a globally defined classical solution whenever the prescribed initial data are suitably regular and satisfy appropriate positivity assumptions. In the present study it is shown that if β < 1, then any such solution is uniformly bounded. This complements a recent result which in the case ρ = 0 has asserted the existence of unbounded solutions whenever β > 1 .