TY  - BOOK
AU  - Iorio Jr, Rafael José
AU  - Iorio, Valeria de Magalhaes
TI  - Fourier analysis and partial differential equations
SN  - 9780521629096
U1  - 515.2433 23rd
PY  - 2001///
CY  - Cambridge
PB  - CUP
KW  - Mathematics
KW  - Differential and Integral Equations
KW  - Dynamical Systems and Control Theory
KW  - Abstract Analysis
N2  - This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and 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. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting 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 non-periodic setting, concentrating on problems that do not occur in the periodic case.

Includes appendix, bibliography and index
ER  -