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 approachesprovides a better alternative to the well-knownindividual-basedandcontinuumones. From a mathematical point of view, the emerging class of systems is charac-terized by the coupling of ordinary and partial differential equations. Generalizingthe hybrid structure of models of the literature, we prove the existence of a weaksolution for the case in which discontinuous functions model the source term ofthe parabolic equation, and we provide also some regularity properties.(c) 2022 Elsevier Ltd. All rights reserved.