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Geometric optics for surface waves in nonlinear elasticity /
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 Vena...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
[2020].
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 1271. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
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| 100 | 1 | |a Coulombel, Jean-François, |e author. | |
| 245 | 1 | 0 | |a Geometric optics for surface waves in nonlinear elasticity / |c Jean-François Coulombel, Mark Williams. |
| 264 | 1 | |a Providence : |b American Mathematical Society, |c [2020]. | |
| 264 | 4 | |c ©2020 | |
| 300 | |a 1 online resource (v, 164 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 0065-9266 ; |v volume 263, number 1271 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Online resource; title from digital title page (viewed on July 08, 2020). | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 e." | |
| 505 | 8 | |a 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 | |a 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 equatio. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Elasticity |x Mathematical models. | |
| 650 | 6 | |a Élasticité |x Modèles mathématiques. | |
| 650 | 7 | |a Elasticidad |x Modelos matemáticos |2 embne | |
| 650 | 7 | |a Elasticity |x Mathematical models |2 fast | |
| 650 | 7 | |a Partial differential equations |x Hyperbolic equations and systems [See also 58J45] |x Nonlinear second-order hyperbolic equations. |2 msc | |
| 650 | 7 | |a Mechanics of deformable solids |x Elastic materials |x Nonlinear elasticity. |2 msc | |
| 650 | 7 | |a Optics, electromagnetic theory {For quantum optics, see 81V80} |x General |x Geometric optics. |2 msc | |
| 700 | 1 | |a Williams, Mark, |e author | |
| 758 | |i has work: |a Geometric optics for surface waves in nonlinear elasticity (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGRDWrmGFkJ8BfjhqDbjmd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: Coulombel, Jean-François. |t Geometric optics for surface waves in nonlinear elasticity. |d Providence, RI : American Mathematical Society, 2020 |z 9781470440374 |w (DLC) 2020023137 |w (OCoLC)1132237716 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1271. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=6176743 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH38606862 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6176743 | ||
| 938 | |a EBSCOhost |b EBSC |n 2439964 | ||
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