Self-similar solutions for nonlinear dispersive equations

• Grant number: 24/15587-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2025
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Thyago Souza Rosa Santos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project aims to study partial differential equations, focusing on the existence,uniqueness, and qualitative properties of special solutions of nonlinear dispersive equations. In particular, we seek to understand the existence, stability, and dynamics of self-similar solutions, as well as the properties of solutions in the vicinity of the selfsimilar region. This is a recent and underexplored topic within the current mathematical community.