Fourier Analysis and its applications to Partial Differential Equations

• Grant number: 09/05185-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2009
• End date: June 30, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Jean Cerqueira Berni
• Host 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.