Fourier Analysis and its applications to Partial Differential Equations

• Grant number: 09/05185-3
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): July 01, 2009
• Effective date (End): June 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Marta Cilene Gadotti
• Grantee: Jean Cerqueira Berni
• Home Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project has the goal of stablish the basic theory of Fourier Analysis, to build results that assure the punctual and uniform convergence and to define the Fourier transform. Then we shall use this theory to describe certain physical phenomena that are modeled through differential partial equations, among them, the problem of the heat conduction in a straight rod, transversal vibrations of a string and the equilibrium of a membrane under the action of certain forces. To these problems, we intend to obtain solutions that also satisfy initial-boundary values conditions, therefore basic notions on the Differential Partial Equations theory shall be developed.