Topics of operators semigroups applied to functional differential equations

• Grant number: 24/23009-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Caroline Barbosa Dias
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

The objective of this research project is to investigate the spectral and self -despair properties associated with linear functional differential equations. Research will focus on the theoretical analysis of the characteristic equation and self -disclaiming of the solutions associated with linear operators in Banach and Hilbert spaces. The focus will be on establishing a profound understanding of the spectral structure of linear operators, such as the infinitesimal generator of semigroups, and the implications of this structure on the solutions of linear functional differential equations.