International Series of Numerical Mathematics

Nonlinear Partial Differential Equations with Applications

Authors: Roubíček, Tomáš

  • Considerably extended second edition of a well-written monograph on modern theory of PDEs
  • Presents theory and applications in a concise, clear, elegant and rigorous way
  • Useful also to engineers, physicists, biologists and other scientists interested in nonlinear differential models
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About this Textbook

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook.

 

The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.

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The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (…) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world.

(Mathematical Reviews)

Reviews

From the reviews of the second edition:

“The monograph is concerned with the study of various classes of nonlinear elliptic and parabolic partial differential equations with many applications. … The book is very well written, the presentation is clear and rigorous, and it contains a comprehensive bibliography. This monograph will be useful to all persons who are interested in nonlinear partial differential equations or systems and their applications.” (Rodica Luca Tudorache, zbMATH, Vol. 1270, 2013)

Table of contents (12 chapters)

  • Preliminary general material

    Roubíček, Tomáš

    Pages 1-27

  • Pseudomonotone or weakly continuous mappings

    Roubíček, Tomáš

    Pages 31-93

  • Accretive mappings

    Roubíček, Tomáš

    Pages 95-114

  • Potential problems: smooth case

    Roubíček, Tomáš

    Pages 115-131

  • Nonsmooth problems; variational inequalities

    Roubíček, Tomáš

    Pages 133-170

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-0348-0513-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-3-0348-0512-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-3-0348-0768-5
  • 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
Nonlinear Partial Differential Equations with Applications
Authors
Series Title
International Series of Numerical Mathematics
Series Volume
153
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0513-1
DOI
10.1007/978-3-0348-0513-1
Hardcover ISBN
978-3-0348-0512-4
Softcover ISBN
978-3-0348-0768-5
Series ISSN
0373-3149
Edition Number
2
Number of Pages
XX, 476
Additional Information
Original edition published by Birkhäuser Verlag, Basel, 2005
Topics