內容簡介
傅立葉分析和偏微分方程This book is the outcome of several courses and seminar talks held at the Instituto de Matematica Pura e Aplicada (IMPA) over the .It is a greatly modified version of a previous work by the authors,Equacoes Diferenciais Parciais, Uma lntroducao, (Projeto Euclides, IMPA,1978). It has a twofold purpose, namely to introduce the student to the basic concepts of Fourier analysis and provide illustrations of recent applications where these concepts were used to study various properties of the solutions of some important nonlinear evolution equations.
目錄
Preface
Part One: Fourier Series and Periodic Distributions
1 Preliminaries
1.1 Basic Definitions and Examples
1.2 Classification into Types
1.3 Boundary and/or Initial Value Problems
1.4 Separation of Variables: Heat Flow in a Bar
1.5 TheSchrodingerand the Wave Equations
1.6 The Dirichlet Problem in the Unit Circle
1.7 Maximum Principles and Uniqueness
2 Fourier Series: Basic Theory
2.1 Spaces of Periodic Functions and Sequences
2.2 The Fourier Transform
2.3 Geometric Interpretation
2.4 Decay and Differentiability
