Existence of solutions for coupled hybrid systems of differential equations for microscopic dynamics and local concentrations

t. Coupled hybrid models, gathering the advantages of multiscale approaches, are nowadays spreading in the field of mathematical models for biological phenomena. The structure of the investigated system arises in modelling collective cell migrations and growth, and particularly fits to those scenarios in which the dynamics of discrete particles is influenced by a continuum chemical concentration. In this paper we focus on existence of solutions in the case of a local concentration. Our construction will rely on approximation techniques, involving a suitable family approximating problems with a nonlocal term in the corresponding Ode, and passage to the lim