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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Coulombel, Jean-François (Autor), Williams, Mark (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, [2020].
Colección:Memoirs of the American Mathematical Society ; no. 1271.
Temas:
Elasticity > Mathematical models.
Élasticité > Modèles mathématiques.
Elasticidad > Modelos matemáticos
Elasticity > Mathematical models
Partial differential equations > Hyperbolic equations and systems [See also 58J45] > Nonlinear second-order hyperbolic equations.
Mechanics of deformable solids > Elastic materials > Nonlinear elasticity.
Optics, electromagnetic theory {For quantum optics, see 81V80} > General > Geometric optics.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 e."
  • 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

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