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Local and Global Analysis of Nonlinear Dispersive and Wave Equations (CBMS Regional Conference Series in Mathematics)

Local And Global Analysis of Nonlinear Dispersive And Wave Equations

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Local and Global Analysis of Nonlinear Dispersive and Wave Equations (CBMS Regional Conference Series in Mathematics)

Local And Global Analysis of Nonlinear Dispersive And Wave Equations

4.85 69,123 ratings · 5,424 reviews
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Overview: Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrodinger 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.

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Pages N/A
Language Eng
Published July 1, 2006
ISBN 996239
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Terence Tao is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Terence Tao can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Cynthia Nguyen
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Michael Rodriguez
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Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Patricia Cruz December 13, 2025
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Anthony Lopez
Anthony Lopez May 20, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
John Rivera
John Rivera November 01, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Betty Green December 30, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Betty Brown October 15, 2025
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Karen Diaz
Karen Diaz June 22, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Margaret Carter
Margaret Carter June 08, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Nicholas Evans
Nicholas Evans April 04, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Stephanie Nguyen August 18, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Ryan Carter September 16, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Stephanie Nguyen April 25, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Charles Green April 04, 2025
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Nancy Nelson
Nancy Nelson August 15, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Eric Martin
Eric Martin April 07, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Kenneth Turner
Kenneth Turner May 22, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Mary Green
Mary Green May 22, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Brian Nguyen
Brian Nguyen June 14, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Edward Hill
Edward Hill December 29, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Sandra Jackson
Sandra Jackson July 11, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Stephanie Thomas
Stephanie Thomas June 25, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Gary Perez
Gary Perez March 03, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Patricia Nelson
Patricia Nelson July 13, 2024
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Eric Martin
Eric Martin September 27, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Brian Harris
Brian Harris October 24, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Laura Adams
Laura Adams April 17, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Nicholas Sanchez
Nicholas Sanchez February 28, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Emily Mitchell
Emily Mitchell November 28, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Ryan Taylor
Ryan Taylor July 11, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Sharon Wright
Sharon Wright July 13, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Joseph King
Joseph King June 14, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Jacob Lewis September 11, 2025
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
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