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

Abstract

This paper deals with an initial-boundary value problem for a doubly haptotactic cross-diffusion system arising from the oncolytic virotherapy [Formula: see text] in a smoothly bounded domain [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. Based on a self-map argument, it is shown that under the assumption [Formula: see text], this problem possesses a uniquely determined global classical solution [Formula: see text] for certain type of small data [Formula: see text]. Moreover, [Formula: see text] is globally bounded and exponentially stabilizes toward its spatially homogeneous equilibrium [Formula: see text] as [Formula: see text].