Fundamental Solutions of Linear Partial Differential Operators Theory and Practice /

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 attent...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Ortner, Norbert (Συγγραφέας), Wagner, Peter (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
Έκδοση:1st ed. 2015.
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Ortner, Norbert.  |e author. 
245 1 0 |a Fundamental Solutions of Linear Partial Differential Operators  |h [electronic resource] :  |b Theory and Practice /  |c by Norbert Ortner, Peter Wagner. 
250 |a 1st ed. 2015. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2015. 
300 |a XII, 398 p. 5 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
505 0 |a Introduction -- I. Distributions and Fundamental Solutions -- II. General Principles for Fundamental Solutions -- III. Parameter Integration -- IV. Quasihyperbolic Systems -- V. Fundamental Matrices of Homogeneous Systems -- Appendix: Table of Operators/Systems with References to Fundamental Solutions/Matrices -- References -- Index. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Functional analysis. 
650 0 |a Integral transforms. 
650 0 |a Operational calculus. 
650 0 |a Partial differential equations. 
650 1 4 |a Mathematics. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Integral Transforms, Operational Calculus. 
650 2 4 |a Functional Analysis. 
700 1 |a Wagner, Peter.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783319201399 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-20140-5  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)