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Fundamental solutions of linear partial differential operators = theory and practice /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Fundamental solutions of linear partial differential operators/ by Norbert Ortner, Peter Wagner.
Reminder of title:	theory and practice /
Author:	Ortner, Norbert.
other author:	Wagner, Peter.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xii, 398 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Differential equations, Partial. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-20140-5
ISBN:	9783319201405

Fundamental solutions of linear partial differential operators = theory and practice /
Ortner, Norbert.

Fundamental solutions of linear partial differential operatorstheory and practice /[electronic resource] :by Norbert Ortner, Peter Wagner. - Cham :Springer International Publishing :2015. - xii, 398 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783319201405

Standard No.: 10.1007/978-3-319-20140-5doiSubjects--Topical Terms:

527784
Differential equations, Partial.

LC Class. No.: QA274.75

Dewey Class. No.: 519.233

Fundamental solutions of linear partial differential operators = theory and practice /
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245 1 0 $a Fundamental solutions of linear partial differential operators $h [electronic resource] : $b theory and practice / $c by Norbert Ortner, Peter Wagner.
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300 $a xii, 398 p. : $b ill., digital ; $c 24 cm.
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 Differential equations, Partial. $3 527784
650 0 $a Diffusion processes. $3 527826
650 0 $a Differential equations, Elliptic. $3 563985
650 0 $a Differential equations, Parabolic. $3 528402
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Integral Transforms, Operational Calculus. $3 672154
650 2 4 $a Functional Analysis. $3 672166
700 1 $a Wagner, Peter. $3 1067993
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