Fundamental solutions of linear partial differential operators : theory and practice / by Norbert Ortner, Peter Wagner.

Format:

Book

Author/Creator:

Ortner, Norbert., Author.

Wagner, Peter, Author.

Language:

English

Subjects (All):

Differential equations, Partial.

Integral transforms.

Calculus, Operational.

Functional analysis.

Partial Differential Equations.

Integral Transforms, Operational Calculus.

Functional Analysis.

Local Subjects:

Partial Differential Equations.

Integral Transforms, Operational Calculus.

Functional Analysis.

Physical Description:

1 online resource (407 p.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

3-319-20140-9