Geometric Optics for Surface Waves in Nonlinear Elasticity. (Record no. 17670)
[ view plain ]
| 000 -LEADER | |
|---|---|
| fixed length control field | 04844nam a22004573i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6176743 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114212.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s1920 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470456504 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470440374 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6176743 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6176743 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1151184105 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QC383 |
| Item number | .C685 2020 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 530.4/16 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Coulombel, Jean-François. |
| 245 10 - TITLE STATEMENT | |
| Title | Geometric Optics for Surface Waves in Nonlinear Elasticity. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 1920. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©1920. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (164 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.263 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. General introduction -- Chapter 2. Derivation of the weakly nonlinear amplitude equation -- 2.1. The variational setting: assumptions -- 2.2. Weakly nonlinear asymptotics -- 2.3. Isotropic elastodynamics -- 2.4. Well-posedness of the amplitude equation -- Chapter 3. Existence of exact solutions -- 3.1. Introduction -- 3.2. The basic estimates for the linearized singular systems -- 3.3. Uniform time of existence for the nonlinear singular systems -- 3.4. Singular norms of nonlinear functions -- 3.5. Uniform higher derivative estimates and proof of Theorem 3.7 -- 3.6. Local existence and continuation for the singular problems with \eps fixed -- Chapter 4. Approximate solutions -- 4.1. Introduction -- 4.2. Construction of the leading term and corrector -- Chapter 5. Error Analysis and proof of Theorem 3.8 -- 5.1. Introduction -- 5.2. Building block estimates -- 5.3. Forcing estimates -- 5.4. Estimates of the extended approximate solution -- 5.5. Endgame -- Chapter 6. Some extensions -- 6.1. Extension to general isotropic hyperelastic materials. -- 6.2. Extension to wavetrains. -- 6.3. The case of dimensions ≥3. -- Appendix A. Singular pseudodifferential calculus for pulses -- A.1. Symbols -- A.2. Definition of operators and action on Sobolev spaces -- A.3. Adjoints and products -- A.4. Extended calculus -- A.5. Commutator estimates -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as "the amplitude equation", is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions u^{\varepsilon} to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength \varepsilon , and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to u^{\varepsilon} on a time interval independent of \varepsilon . This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Williams, Mark. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Coulombel, Jean-François |
| Title | Geometric Optics for Surface Waves in Nonlinear Elasticity |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c1920 |
| International Standard Book Number | 9781470440374 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6176743">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6176743</a> |
| Public note | Click to View |
No items available.