Existence of solutions for hybrid systems of differential equations under exogenous information with discontinuous source term. (August 2022)

• Record Type: Journal Article
• Authors: Menci, Marta; Papi, Marco
• Is Part Of: Nonlinear analysis. Volume 221(2022)
• Publication Date: 2022-08
• Subjects: Hybrid models -- Chemotaxis -- Parabolic equation -- Discontinuous source term; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112885
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.