Authors:
Overview on general existence and uniqueness theorems for fundamental solutions
Rigorous derivation and verification of fundamental solutions and matrices without the usual recourse to physical intuition
Presentation of new methods like parameter integration and reduction of 3-fold integrals for constructing fundamental solutions
Includes supplementary material: sn.pub/extras
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
This monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions.
The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals.
In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell’s system and others.
The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.
Reviews
“The monograph is written in a concise style with rigorous proofs and precise reference to the corresponding literature … . Any topic is motivated and explained by concrete applications to equations and systems coming from physics. … In conclusion, the monograph of Ortner and Wagner is highly recommended to everyone interested in distribution theory and explicit formulas for elementary solutions.” (Michael Langenbruch, zbMATH 1336.35003, 2016)
Authors and Affiliations
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Department of Mathematics, University of Innsbruck, Innsbruck, Austria
Norbert Ortner
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Faculty of Engineering Science, University of Innsbruck, Innsbruck, Austria
Peter Wagner
Bibliographic Information
Book Title: Fundamental Solutions of Linear Partial Differential Operators
Book Subtitle: Theory and Practice
Authors: Norbert Ortner, Peter Wagner
DOI: https://doi.org/10.1007/978-3-319-20140-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-20139-9Published: 17 August 2015
Softcover ISBN: 978-3-319-36799-6Published: 22 October 2016
eBook ISBN: 978-3-319-20140-5Published: 05 August 2015
Edition Number: 1
Number of Pages: XII, 398
Number of Illustrations: 5 b/w illustrations
Topics: Partial Differential Equations, Integral Transforms, Operational Calculus, Functional Analysis