Non-Linear Partial Differential Equations - 1st Edition - ISBN: 9780444887009, 9780080872759

Non-Linear Partial Differential Equations, Volume 164

1st Edition

An Algebraic View of Generalized Solutions

Authors: E.E. Rosinger
Hardcover ISBN: 9780444887009
eBook ISBN: 9780080872759
Imprint: North Holland
Published Date: 22nd November 1990
Page Count: 379
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Table of Contents

  1. Conflict Between Discontinuity, Multiplication and Differentiation. 2. Global Version of the Cauchy Kovalevskaia Theorem on Analytic Nonlinear Partial Differential Equations. 3. Algebraic Characterization for the Solvability of Nonlinear Partial Differential Equations. 4. Generalized Solutions of Semilinear Wave Equations with Rough Initial Values. 5. Discontinuous, Shock, Weak and Generalized Solutions of Basic Nonlinear Partial Differential Equations. 6. Chains of Algebras of Generalized Functions. 7. Resolution of Singularities of Weak Solutions for Polynomial Nonlinear Partial Differential Equations. 8. The Particular Case of Colombeau's Algebras. Final Remarks. References.

Description

  1. Conflict Between Discontinuity, Multiplication and Differentiation. 2. Global Version of the Cauchy Kovalevskaia Theorem on Analytic Nonlinear Partial Differential Equations. 3. Algebraic Characterization for the Solvability of Nonlinear Partial Differential Equations. 4. Generalized Solutions of Semilinear Wave Equations with Rough Initial Values. 5. Discontinuous, Shock, Weak and Generalized Solutions of Basic Nonlinear Partial Differential Equations. 6. Chains of Algebras of Generalized Functions. 7. Resolution of Singularities of Weak Solutions for Polynomial Nonlinear Partial Differential Equations. 8. The Particular Case of Colombeau's Algebras. Final Remarks. References.

Details

No. of pages:
379
Language:
English
Copyright:
© North Holland 1990
Published:
Imprint:
North Holland
eBook ISBN:
9780080872759

Reviews

@qu:The author of this volume proposes a systematic and wide-ranging nonlinear theory of GF's, based on differential algebras, applicable to a very broad class of NLPDE's. He also provides an excellent historical survey and derives some new results. @source:ASLIB Book List


About the Authors

E.E. Rosinger Author

Affiliations and Expertise

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa