Iorio R.J., de Magalhaes Iorio V. Fourier Analysis and Partial Differential Equations: An Introduction

UK: Cambridge University Press, 2001. — 419 p. — (Cambridge Studies in Advanced Mathematics 70). — ISBN-0-521-62116-X.This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations, including a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations; they turn their attention, in the two final chapters, to the nonperiodic setting, concentrating on problems that do not occur in the periodic case.Fourier Series and Periodic Distributions
Preliminaries
Fourier Series: Basic Theory
Periodic Distributions and Sobolev Spaces
Applications to Partial Differential Equations
Linear Equations
Nonlinear Evolution Equations
Nonperiodic Problems
Distributions, Fourier Transform and Linear Equationspp KdV, BO and Friends
Appendixes
Tools from the Theory of ODE
Commutator Estimates