Equação da onda: soluções de problemas de valores iniciais e de fronteira a partir da análise de Fourier

Abstract

In this work, we will study the Wave Equation, an important equation in the study of Partial Differential Equations. We will work on problems involving the finite-string wave equation with fixed ends, the infinite string, and the semi-infinite string. However, to get to such problems, we will need to do a study about the Fourier Series, studying the convergence of such series, so we will need some Real Analysis. In addition, we will study some important inequalities such as: Bessel Inequality, Cauchy-Schwarz Inequality and Minkowski Inequality. For that, we have a basis for solving the EDP’s in question.