Viability in a non-local population model structured by size and spatial position

Abstract

Motivated conceptually by multiscale models of cancer cell migration, the focus is on a broad class of set-valued population models structured both physiologically and spatially. For time-dependent sets of constraints given, sufficient conditions are provided such that every permitted density function initializes at least one admissible weak solution. This result about viability a.k.a. weak invariance concerns non-local hyperbolic differential inclusions of first order with memory and with one boundary condition for the minimal value of the scalar structure parameter.