| Description |
1 online resource (v, 164 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 263, number 1271 |
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Memoirs of the American Mathematical Society ; no. 1271.
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| Contents |
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 |
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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." |
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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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from digital title page (viewed on July 08, 2020) |
| Subject |
Elasticity -- Mathematical models
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Elasticidad -- Modelos matemáticos
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Elasticity -- Mathematical models
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Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations.
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Mechanics of deformable solids -- Elastic materials -- Nonlinear elasticity.
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Optics, electromagnetic theory {For quantum optics, see 81V80} -- General -- Geometric optics.
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| Form |
Electronic book
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| Author |
Williams, Mark, author
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| ISBN |
1470456508 |
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9781470456504 |
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