Exact and Asymptotic Solutions of the Cauchy Problem (Classic Reprint) - Couverture souple

Ludwig, Donald

9781332942855: Exact and Asymptotic Solutions of the Cauchy Problem (Classic Reprint)

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ISBN 10 : 1332942857 ISBN 13 : 9781332942855

Editeur : Forgotten Books, 2018

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Explore how advanced math explains waves, echoes, and sharp turns in the Cauchy problem. This readable study applies geometric optics ideas to linear hyperbolic systems, showing how singular data evolve, how caustics form, and how to build solutions from progressing waves and plane-wave superpositions. With clear development from theory to concrete techniques, the book reveals when and why asymptotic expansions converge and how fundamental solutions arise.

The work outlines practical methods for handling problems with distribution data, including how to extend solutions beyond caustics and how to interpret wave behavior through rays, envelopes, and phase functions. It connects abstract concepts to structured procedures you can apply to similar hyperbolic systems, providing a toolkit for researchers and advanced students.

- Grasp the idea of progressing waves and generalized progressing waves, and how they help manage singular initial data.
- Learn how caustics affect asymptotic solutions and how envelopes extend the reach of solutions.
- See how the Riemann function and fundamental solutions are constructed and interpreted.
- Follow step-by-step approaches to derive transport equations and analyze wave distortion along rays.

Ideal for readers of advanced applied mathematics, partial differential equations, and mathematical physics who want a rigorous, practical treatment of wave propagation and Cauchy problems.

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�diteur: Forgotten Books
Date d'�dition: 2018
Langue: anglais
ISBN 10: 1332942857
ISBN 13: 9781332942855
Reliure: Broch�
Nombre de pages: 105
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Exact and Asymptotic Solutions of the Cauchy Problem (Classic Reprint)

Donald Ludwig

Edit� par Forgotten Books, 2018

ISBN 10 : 1332942857 ISBN 13 : 9781332942855

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Vendeur : Forgotten Books, London, Royaume-Uni

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Paperback. Etat : New. Print on Demand. This book presents a theoretical framework for examining linear hyperbolic partial differential equations. It provides a foundation for understanding the Cauchy problem, which seeks to determine a solution to such equations subject to specified initial conditions. The author, an established mathematician, employs a novel approach called 'generalized progressing wave solutions' to construct explicit solutions to these equations, even when the initial data is singular. The book's significance lies in extending the methods of geometrical optics to a much broader class of problems, offering a deeper understanding of the behavior of solutions to hyperbolic equations, including the phenomenon of caustics, where the usual solution techniques break down. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. N� de r�f. du vendeur 9781332942855_0

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