A Nonlinear Theory of Generalized Functions. 1st ed. 1990

種類:

電子ブック

責任表示:

by Hebe de Azevedo Biagioni

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1990

著者名:

• Biagioni, Hebe de Azevedo.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1421

ISBN:

9783540469810 [3540469818]    

注記:

Generalized functions on an open subset of En -- Generalized functions on an arbitrary subset of En -- Generalized solutions of nonlinear partial differential equations.
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 applicati

ローカル注記:

学内専用E-BOOKS (local access only)