Applied Mathematical Sciences

Partial Differential Equations III

Nonlinear Equations

Authors: Taylor, Michael

  • Three volumes offer complete reference to PDEs
  • Includes both theory and applications
  • Lots of examples and exercises
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About this book

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. In this second edition, there are seven new sections including Sobolev spaces on rough domains, boundary layer phenomena for the heat equation, an extension of complex interpolation theory, and Navier-Stokes equations with small viscosity. In addition, several other sections have been substantially rewritten, and numerous others polished to reflect insights obtained through the use of these books over time. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(SIAM Review, June 1998)

About the authors

Michael E. Taylor is a Professor at University of North Carolina in the Department of Mathematics.

Reviews

From the reviews:

“These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(SIAM Review, June 1998)

From the reviews of the second edition:

“This substantial three-volume work is an upgraded version of the comprehensive qualitative analysis of partial differential equations presented in the earlier edition. … Graduate students … will find these three volumes to be not just a fine and rigorous treatment of the subject, but also a source of inspiration to apply their knowledge and ability to the solution of other challenging problems in the field of partial differential equations. … an excellent text for all devotees of the charming and thought-provoking byways of higher mathematics.” (Christian Constanda, The Mathematical Association of America, July, 2011)


Table of contents (6 chapters)

  • Function Space and Operator Theory for Nonlinear Analysis

    Taylor, Michael E.

    Pages 1-104

  • Nonlinear Elliptic Equations

    Taylor, Michael E.

    Pages 105-311

  • Nonlinear Parabolic Equations

    Taylor, Michael E.

    Pages 313-411

  • Nonlinear Hyperbolic Equations

    Taylor, Michael E.

    Pages 413-529

  • Euler and Navier—Stokes Equations for Incompressible Fluids

    Taylor, Michael E.

    Pages 531-614

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-1-4419-7049-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-1-4419-7048-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $209.00
price for USA
  • ISBN 978-1-4614-2741-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Partial Differential Equations III
Book Subtitle
Nonlinear Equations
Authors
Series Title
Applied Mathematical Sciences
Series Volume
117
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-7049-7
DOI
10.1007/978-1-4419-7049-7
Hardcover ISBN
978-1-4419-7048-0
Softcover ISBN
978-1-4614-2741-4
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XXII, 715
Topics