Existence of solutions for hybrid systems of differential equations under exogenous information with discontinuous source term

In the mathematical modeling framework, the adoption of multiscale approaches provides a better alternative to the well-known individual-based and continuum ones. From a mathematical point of view, the emerging class of systems is characterized by the coupling of ordinary and partial differential equations. Generalizing the hybrid structure of models of the literature, we prove the existence of a weak solution for the case in which discontinuous functions model the source term of the parabolic equation, and we provide also some regularity properties.