Fourier analysis and partial differential equations
著者
書誌事項
Fourier analysis and partial differential equations
（Cambridge studies in advanced mathematics, 70）
Cambridge University Press, 2012
- : pbk
大学図書館所蔵 件 / 全6件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 401-408) and index
内容説明・目次
内容説明
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 Schroedinger 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.
目次
- 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.
「Nielsen BookData」 より
