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Fundamental solutions of linear partial differential operators[electronic resource] :theory and practice /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	519.233
書名/作者:	Fundamental solutions of linear partial differential operators : theory and practice // by Norbert Ortner, Peter Wagner.
作者:	Ortner, Norbert.
其他作者:	Wagner, Peter.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xii, 398 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
標題:	Diffusion processes.
標題:	Differential equations, Elliptic.
標題:	Differential equations, Parabolic.
標題:	Mathematics.
標題:	Partial Differential Equations.
標題:	Integral Transforms, Operational Calculus.
標題:	Functional Analysis.
ISBN:	9783319201405
ISBN:	9783319201399
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-20140-5

Fundamental solutions of linear partial differential operators[electronic resource] :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:

389324
Differential equations, Partial.

LC Class. No.: QA274.75

Dewey Class. No.: 519.233

Fundamental solutions of linear partial differential operators[electronic resource] :theory and practice /
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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.
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