Some Uniqueness Theorems for the Reduced Wave Equation (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 18.43
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book completes and extends the Magnus-Rellich uniqueness theorem for the reduced wave equation in infinite domains, including piece-wise smooth boundaries and mixed boundary conditions. No auxiliary "edge conditions" are required at edges or discontinuities in the boundary conditions; continuity of the wave function in the closure of the domain is sufficient. This extension allows several interesting problems in diffraction theory, such as diffraction by a disk of zero thickness or a semi-infinite circular cone. The original uniqueness theorem for the reduced wave equation in infinite domains was stated by Sommerfeld, and first proved by Magnus. The elimination of an extraneous "finiteness condition" was accomplished by Rellich, resulting in the theorem stated above. The author extends the theorem to include a considerably more general class of finite boundaries and infinite boundaries, and boundaries with singularities of the type occurring at the apex of a (generalized) cone. The extension to infinite boundaries is limited to the case where the domain is "eventually conical", i.e. outside a sufficiently large sphere, it is generated by a ray emanating from the center. This book represents a significant contribution to the field of diffraction theory, providing a more general and flexible framework for analyzing wave phenomena in complex domains. 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.…
Seller Inventory # 9781330155424_0
- Title
- Some Uniqueness Theorems for the Reduced Wave Equation (Classic Reprint)
- Author
- Leo M. Levine
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1330155424
- ISBN 13
- 9781330155424
- Seller catalogs
- Calculus
Discover how the reduced wave equation behaves in complex domains and why boundary conditions matter for uniqueness.
This book examines foundational results about when a solution to the reduced wave equation is uniquely determined by its values and boundary data. It discusses extensions of classical theorems to more general shapes, such as exterior domains, finite and infinite boundaries, and surfaces with singularities. The material focuses on practical implications for diffraction theory, including how different boundary conditions influence existence and uniqueness.
- See how exterior domains and regular closed surfaces shape uniqueness results.
- Learn about alternative radiation conditions and their weaker forms.
- Understand how mixed boundary conditions extend classic theorems for diffraction problems.
- Explore how infinite boundaries and conical singularities are handled in the theory.
"Synopsis" may belong to another edition of this title.
Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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