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Catalogue Information
Field name	Details
Dewey Class	515
Title	A Nonlinear Theory of Generalized Functions ([EBook] /) / edited by Hebe de Azevedo Biagioni.
Added Personal Name	Biagioni, Hebe de Azevedo editor.
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1990.
Physical Details	XIV, 218 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1421
ISBN	9783540469810
Summary Note	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.:
Contents note	Generalized functions on an open subset of En -- Generalized functions on an arbitrary subset of En -- Generalized solutions of nonlinear partial differential equations.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0089552
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Biagioni, Hebe de Azevedo . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515 .

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A Nonlinear Theory of Generalized Functions

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