On Abstract explicit neutral differential equations with space-time dependent argument

• Grant number: 25/00262-2
• Support Opportunities: Scholarships abroad - Research
• Start date: June 23, 2025
• End date: September 29, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Alex Hernández Morales
• Grantee: Eduardo Alex Hernández Morales
• Host Investigator: Jianhong Wu
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Institution abroad: York University, Canada

Abstract

The fundamental objective of this project is the introduction of the theory of differential equations with space-time-state dependent arguments by means of the study of abstract neutral explicit differential equations with applications to partial differential equations. This new theory of differential equations will allow the generalization of an extensive literature on different classes of integral and differential equations with temporal delay. Considering the abstract and complex formulation of the neutral problem considered in this project, we note that the ideas and techniques to be developed in this project can be used in the study of ordinary differential equations in finite and infinite dimensional spaces, of different models of neutral differential equations and partial evolution differential equations. Furthermore, this new theory is motivated by different important applications.