Finite fractal dimension for non-linear parabolic equations with subdifferential principal part

• Grant number: 22/13001-4
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: February 01, 2023
• End date: January 25, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Alexandre Nolasco de Carvalho
• Grantee: Heraclio Ledgar López Lázaro
• Supervisor: Tomas Caraballo Garrido
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Sevilla (US), Spain
• Associated to the scholarship: 21/01931-4 - Pullback attractor for non-linear parabolic equations with subdifferential principal part, BP.PD

Abstract

This research project deals with the study of the dynamics of solutions, and the estimation of the fractal dimension of the attractors associated with a class of non-linear parabolic equations where the sub differential main part is a non-linear maximal monotone operator and the convective term is a non-monotone, non-Lipschitz operator defined in a dense subset of a Hilbert space. The theory to be developed will allow us to estimate the fractal dimension of attractors associated with multi-valued semigroups. In particular, it will be of interest to apply these results to a class of incompressible non-Newtonian fluids. (AU)