A nonlinear theory of generalized functions /

A nonlinear theory of generalized functions /

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Bibliographic Details
Author / Creator:	Biagioni, Hebe A. (Hebe Azevedo), 1952-
Imprint:	Berlin ; New York : Springer-Verlag, ©1990.
Description:	1 online resource (xii, 214 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 0075-8434 ; 1421 Lecture notes in mathematics (Springer-Verlag) ; 1421.
Subject:	Theory of distributions (Functional analysis) Nonlinear theories. Nonlinear theories. Theory of distributions (Functional analysis)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11071259

Hidden Bibliographic Details
ISBN:	9783540469810 3540469818 9780387524085 0387524088 9783540524083 3540524088
Notes:	Includes bibliographical references (pages 201-211) and index. Restrictions unspecified Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 digitized 2010 HathiTrust Digital Library committed to preserve Print version record.
Summary:	This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.
Other form:	Print version: Biagioni, Hebe A. (Hebe Azevedo), 1952- Nonlinear theory of generalized functions. Berlin ; New York : Springer-Verlag, ©1990

Description
Summary:	This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.
Physical Description:	1 online resource (xii, 214 pages) : illustrations.
Format:	Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Bibliography:	Includes bibliographical references (pages 201-211) and index.
ISBN:	9783540469810 3540469818 9780387524085 0387524088 9783540524083 3540524088
ISSN:	0075-8434 ;