Local And Global Analysis of Nonlinear Dispersive And Wave Equations pdf epub mobi txt 電子書 下載 2024
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发表于2024-11-16
Local And Global Analysis of Nonlinear Dispersive And Wave Equations epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024
Local And Global Analysis of Nonlinear Dispersive And Wave Equations epub 下載 mobi 下載 pdf 下載 txt 電子書 下載 2024
Local And Global Analysis of Nonlinear Dispersive And Wave Equations pdf epub mobi txt 電子書 下載 2024
圖書描述
Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations.
Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.
As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.
著者簡介
圖書目錄
Local And Global Analysis of Nonlinear Dispersive And Wave Equations pdf epub mobi txt 電子書 下載
用戶評價
陶哲軒神作
評分陶哲軒神作
評分陶哲軒神作
評分陶哲軒神作
評分因為想瞭解nonlinear wave選瞭這本書，但不是個明智的選擇，尤其在沒學過調和分析的情況下。但Tao很有洞見，尤其第一章所錶述的內容和之後章節的聯係。細節太少，typo多到後來不想去看勘誤錶，過多的例子和證明放在瞭練習。初學者可以參考Tadahiro Oh "Nonlinear Schrödinger Equations"這門課的筆記和references。 E. L. 認為最後一章關於wave maps的內容過於陳舊。
讀後感
" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...
評分" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...
評分" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...
評分" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...
評分" My personal philosophy that to truly understand a mathematical result one must view it from as many perspectives as possible (including both rigorous arguments and informal heuristics), and must also be able to translate easily from one perspective to an...
Local And Global Analysis of Nonlinear Dispersive And Wave Equations pdf epub mobi txt 電子書 下載 2024
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