Overview
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.
Full Product Details
Author: Norbert Ortner ,
Peter Wagner
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: Softcover reprint of the original 1st ed. 2015
Dimensions:
Width: 15.50cm
, Height: 2.10cm
, Length: 23.50cm
Weight: 6.204kg
ISBN: 9783319367996
ISBN 10: 3319367994
Pages: 398
Publication Date: 22 October 2016
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
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)
“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)
