Authors:
- A unique collection of fully solved long problems, offering a hands-on approach to learning the subject
- Covers the key classical equations: heat, wave, Schrödinger, Monge-Ampère, Euler, Navier-Stokes
- Background on functional analysis, distributions and functional spaces is covered in the problems
Part of the book series: Universitext (UTX)
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Table of contents (10 chapters)
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Front Matter
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Solutions of the Problems and Classical Results
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Front Matter
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Back Matter
About this book
Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory.
Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject.
Reviews
“Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in partial differential equations may find this work useful as a summary of analytic theories published in this volume.” (Vicenţiu D. Rădulescu, zbMATH 1461.35001, 2021)
Authors and Affiliations
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École Normale Supérieure Paris-Saclay, Université Paris-Saclay, Gif sur Yvette, France
Thomas Alazard
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Institut de Mathématique d’Orsay, Université Paris-Saclay, Orsay, France
Claude Zuily
About the authors
Claude Zuily received his PhD from Université Paris-Sud (Orsay), where he was professor of mathematics until 2010. Currently emeritus professor at Université Paris-Saclay, he is the author of several books: Uniqueness and non uniqueness in the Cauchy problem (Birkhäuser 1983), Problèmes de distributions et d'équations aux dérivées partielles (Hermann 1995 and Cassini 2010), Analyse pour l'agrégation (with H. Queffélec) (Dunod 1995), Distributions et équations aux dérivées partielles (Dunod 2002). His primary areas of research are linear and nonlinear partial differentialequations.
Bibliographic Information
Book Title: Tools and Problems in Partial Differential Equations
Authors: Thomas Alazard, Claude Zuily
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-030-50284-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-50283-6Published: 20 October 2020
eBook ISBN: 978-3-030-50284-3Published: 19 October 2020
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 357
Number of Illustrations: 1 b/w illustrations
Topics: Analysis, Functional Analysis, Fourier Analysis, Potential Theory