Degenerate parabolic-hyperbolic equations and averaging lemmas

• Grant number: 21/01800-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2021
• End date: February 28, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Martins dos Santos
• Grantee: João Fernando da Cunha Nariyoshi
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The main goal of the project is to continue the investigation of the theory of "averaging lemmas" and apply it to concrete problems involving degenerate parabolic-hyperbolic equations. More specifically, for these equations, it is intended to study an initial value problem for a stochastic version with periodic boundary conditions, to investigate Sobolev's regularity of entropy and kinetic solutions for deterministic and stochastic variants and to analyze boundary value problems. (AU)