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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.

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