圖書標籤: PDE  數學  nonlinear  色散方程  偏微分方程7  monograph  math  Math   

喜歡 Local And Global Analysis of Nonlinear Dispersive And Wave Equations 的讀者還喜歡

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陶哲軒神作

要讀通的話難度很大。很多習題是著名文章的結果，隻是讓讀者去查找文獻。內容講得真的很好，臨界色散方程的基本方法一應俱全。但不應“僅僅通過”這本書來學習色散方程的基礎知識，主要還是去讀原始文章。 可惜接下來若乾年都與色散方程無緣瞭，不過它的附錄我仍然經常查閱。無論如何，我永遠也不會忘記這本書當初給我帶來的震撼。

PDE的代數（對稱，守恒律，顯示錶達）和分析（漸進，存在和唯一）；方程的幾何物理直覺和嚴格分析之間平衡。自治方程=時間平移不變量=嵌入；第一章一階擬綫性方程組的柯西問題關鍵概念是解析性；諾特定理本質聯係瞭對稱和守恒；

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。

PDE的代數（對稱，守恒律，顯示錶達）和分析（漸進，存在和唯一）；方程的幾何物理直覺和嚴格分析之間平衡。自治方程=時間平移不變量=嵌入；第一章一階擬綫性方程組的柯西問題關鍵概念是解析性；諾特定理本質聯係瞭對稱和守恒；

" 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...

" 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...

" 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...

" 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...

" 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...