Abstract diferential equations with state dependent delay

• Grant number: 21/12559-9
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2022
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Alex Hernández Morales
• Grantee: Eduardo Alex Hernández Morales
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated researchers: Jianhong Wu ; Tomás Caraballo Garrido

Abstract

In this project we will study the local and global existence, the uniqueness and the qualitative properties of solutions for abstract and partial functional differential equations with state dependent delay. The project has two basic objectives. At first, introduce the study of abstract neutral explicit differential equations with state dependent delay, equations with delay terms of the form u'(v(t,u(t))). This part of the project is a natural continuation of my recent works and research activities with Jianhog Wu of the York University, Canada, on abstract differential equations with state-dependent delay. The profesor Wu is an associated reseach of this project. In addition to the above, in this project we will introduce to the literature the study of Navier-Stokes equations with state-dependent delay. This part of the project will be developed with Tomas Caraballo of the Sevilla University, Spain, an important research in differential equations. I note that Caraballo wrote the first work on Navier-Stokes equations with delay. To develop this part of the project, I will request financial support to develop a short research visit to the Sevilla University. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HERNANDEZ, EDUARDO; WU, JIANHONG. Explicit abstract neutral differential equations with state-dependent delay: Existence, uniqueness and local well-posedness. Journal of Differential Equations, v. 365, p. 62-pg., 2023-05-24. (21/12559-9)

HERNANDEZ, EDUARDO. ON EXPLICIT ABSTRACT NEUTRAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY. Proceedings of the American Mathematical Society, v. 151, n. 3, p. 15-pg., 2023-03-01. (21/12559-9)