Wave equation: weak solution and energy decay

• Grant number: 21/05630-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2021
• End date: August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Bianca Morelli Rodolfo Calsavara
• Grantee: Vítor Misso
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 19/02512-5 - Systems and partial differential equations, AP.TEM

Abstract

This project basically consists of two parts. In the first, introductory topics of measurement and integration theory, $L^{p}$ and $L^{\ infty}$ spaces, Sobolev spaces and some time-dependent spaces will be studied. And in the second part it will be studied the existence and uniqueness of weak solution for the wave equation and for a hyperbolic equation with damping term, in addition to the energy decay for these equations. (AU)