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International Series of Numerical Mathematics

Nonlinear Partial Differential Equations with Applications

Authors: Roubicek, Tomás

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About this Textbook

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. It balances the abstract functional-analysis approach based on nonlinear monotone, pseudomonotone, weakly continuous, or accretive mappings with concrete partial differential equations in their weak (or more general) formulation. Methods of Galerkin or of Rothe are exposed in a large generality. Other methods include various direct methods, regularization, or fixed points. The exposition leads general theory as fast as possible towards the analysis of concrete 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 rather an introduction into the subject while some others form an advanced textbook. The intended audience is graduate and PhD students and researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems.

Reviews

From the reviews:

"The book under review is mainly devoted to the study of both steady-state (Part I) and evolution (Part II) boundary value problems … . The organization of the material is well done, and the presentation … is clear, elegant and rigorous. … In conclusion, primarily addressed to graduate and Ph.D. students and researchers … this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists … ." (Ioan I. Vrabie, Mathematical Reviews, Issue 2007 e)


Table of contents (12 chapters)

Table of contents (12 chapters)
  • Preliminary general material

    Pages 1-26

  • Pseudomonotone or weakly continuous mappings

    Pages 29-87

  • Accretive mappings

    Pages 89-108

  • Potential problems: smooth case

    Pages 109-124

  • Nonsmooth problems; variational inequalities

    Pages 125-160

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-7643-7397-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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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
2005
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7397-9
DOI
10.1007/3-7643-7397-0
Series ISSN
0373-3149
Edition Number
1
Number of Pages
XVIII, 405
Topics