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Lectures on Nonlinear Hyperbolic Differential Equations (Mathématiques et Applications) 1997th Edition

4 out of 5 stars 1 customer review
ISBN-13: 978-3540629214
ISBN-10: 3540629211
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Product Details

  • Series: Mathématiques et Applications (Book 26)
  • Paperback: 290 pages
  • Publisher: Springer; 1997 edition (December 17, 2003)
  • Language: English
  • ISBN-10: 3540629211
  • ISBN-13: 978-3540629214
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 14.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,585,696 in Books (See Top 100 in Books)

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Hörmanders book in this subject is interesting, very interesting. Partly because it addresses nonlinear hyperbolic operators, and that is unusual. Almost any book in this subject would stay with the linear setting, and the hyperbolic non-linear notion is very tied to the field equations of Quantum Field Theory(QFT), which are usually hyperbolic and non-linear. A propagating wave after a boat follows a hyperbolic equation, and it is natural to ask what would have if we deform it to a non-linear hyperbolic problem. Much the same in QFT, where equations like the Dirac equation and the, of course non-linear, Yang-Mills equation are hyperbolic in Minkowski space-time or for that manner on any pseudo-Riemannian manifold of appropriate singnature.

Now, physicists usually attack this via a holomorphic perspective on elliptic problems, where as many mathematicans would look at the relevant Cauchy problem, which may also be overdetermined or behave differently in different settings. There are very big differences between the elliptic and hyperbolic setting for non-linear operators(Indeed there are very large differences even in the linear setting.). The questions that arise are very delicate. And it is here that this book comes into play. Read it!
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