Fourier Analysis and Partial Differential Equations

ISBN-13: 9780521621168 / Angielski / Twarda / 2001 / 424 str.

JR Rafael Jose Iorio; Rafael Jose Iorio Jr; Jr. Iorio

Opis

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 Schrodinger 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.

Recenzje

'Students and those beginning their academic career should find this text interesting and stimulating.' European Mathematical Society Newsletter

Spis treści

Part I. Fourier Series and Periodic Distributions: 1. Preliminaries; 2. Fourier series: basic theory; 3. Periodic distributions and Sobolev spaces; Part II. Applications to Partial Differential Equations: 4. Linear equations; 5. Nonlinear evolution equations; 6. The Korteweg-de Vries; Part III. Some Nonperiodic Problems: 7. Distributions, Fourier transforms and linear equations; 8. KdV, BO and friends; Appendix A. Tools from the theory of ODEs; Appendix B. Commutator estimates; Bibliography; Index.