Global solutions for a path-dependent hybrid system of differential equations under parabolic signal. (July 2019)

• Record Type: Journal Article
• Authors: Menci, Marta; Papi, Marco
• Is Part Of: Nonlinear analysis. Volume 184(2019)
• Page Start: 172
• Page End: 192
• Publication Date: 2019-07
• Subjects: Hybrid models -- Parabolic differential equation -- Collective motions -- Chemotaxis; 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.2019.01.034
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in which the dynamics of interacting agents are driven by second-order ODEs, while reaction–diffusion equations are used to model the time evolution of a signal influencing them. We first present an existence result of the solution, locally in time. In particular, we generalize the framework of recent works, presented in the literature with a modeling and numerical approach, which have not been investigated from an analytical point of view so far. Then, the previous result is extended in order to obtain a global solution.