Overview
- Balances the abstract functional-analysis approach with concrete partial differential equations
- Methods of Galerkin or of Rothe are exposed in a large generality
- Primarily intended for graduate and PhD students as well as for researchers
- Includes supplementary material: sn.pub/extras
Part of the book series: International Series of Numerical Mathematics (ISNM, volume 153)
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Table of contents (12 chapters)
Keywords
About this book
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)
Authors and Affiliations
Bibliographic Information
Book Title: Nonlinear Partial Differential Equations with Applications
Authors: Tomáš Roubíček
Series Title: International Series of Numerical Mathematics
DOI: https://doi.org/10.1007/3-7643-7397-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2005
eBook ISBN: 978-3-7643-7397-9Published: 17 January 2006
Series ISSN: 0373-3149
Series E-ISSN: 2296-6072
Edition Number: 1
Number of Pages: XVIII, 405
Topics: Difference and Functional Equations, Partial Differential Equations, Computational Mathematics and Numerical Analysis, Numerical Analysis