The Galerkin method and apllications in heat and wave equations

• Grant number: 24/21542-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2025
• End date: November 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Bianca Morelli Rodolfo Calsavara
• Grantee: Isadora Farinacio Camillo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project basically consists of three parts.Firstly, there will be a review of some introductory topics in measurement and integration theory, Lp spaces, Sobolev spaces and some time-dependent spaces.And in the second part, the existence of a weak solution to the heat equation will be studied by using the Galerkin method.Finally, in the third part, the Galerkin method will be used to obtain the existence of a solution for the wave equation. The uniqueness of the solution for the heat and wave equations will also be studied via energy method, in the second and third parts, respectively.