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Fundamental solutions of linear part...

Ortner, Norbert, (1945-)

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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Fundamental solutions of linear partial differential operators :Norbert Ortner, Peter Wagner.
其他題名:	theory and practice /
作者:	Ortner, Norbert,
其他作者:	Wagner, Peter
出版者:	Cham :Springer,c2015.
面頁冊數:	xii, 398 p. ;25 cm.
標題:	Differential equations, Elliptic.
ISBN:	3319201395

Fundamental solutions of linear partial differential operators :theory and practice /
Ortner, Norbert,1945-

Fundamental solutions of linear partial differential operators :theory and practice /Norbert Ortner, Peter Wagner. - Cham :Springer,c2015. - xii, 398 p. ;25 cm.

Includes bibliographical references (p. 383-394) and index.

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: 3319201395

LCCN: 2015947499Subjects--Topical Terms:

205654
Differential equations, Elliptic.

LC Class. No.: QA377 / .O78 2015

Dewey Class. No.: 515.4

Fundamental solutions of linear partial differential operators :theory and practice /
LDR:02398cam a2200241 a 450 001 480031
003 OCoLC
005 20160809225238.0
008 160826s2015 sz b 001 0 eng d
010 $a 2015947499
020 $a 3319201395
020 $a 9783319201399 : $c NT$3069
020 $z 9783319201405 (eBook)
035 $a (OCoLC)909327330
035 $a ocn909327330
040 $a BTCTA $b eng $c BTCTA $d YDXCP $d CDX $d OCLCO $d LYU $d MUU $d IUL
050 4 $a QA377 $b .O78 2015
082 0 4 $a 515.4 $2 23
100 1 $a Ortner, Norbert, $d 1945- $e author. $3 735554
245 1 0 $a Fundamental solutions of linear partial differential operators : $b theory and practice / $c Norbert Ortner, Peter Wagner.
260 $a Cham : $b Springer, $c c2015.
300 $a xii, 398 p. ; $c 25 cm.
504 $a Includes bibliographical references (p. 383-394) and index.
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, Elliptic. $3 205654
650 0 $a Differential equations, Parabolic. $3 247280
650 0 $a Differential equations, Partial. $3 189753
650 0 $a Diffusion processes. $3 186291
700 1 $a Wagner, Peter $c (Engineer), $e author. $3 735555