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006			m o d |
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008			240724s1920 xx o ||||0 eng d
020			_a9781470456504 _q(electronic bk.)
020			_z9781470440374
035			_a(MiAaPQ)EBC6176743
035			_a(Au-PeEL)EBL6176743
035			_a(OCoLC)1151184105
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQC383 _b.C685 2020
082	0		_a530.4/16
100	1		_aCoulombel, Jean-François.
245	1	0	_aGeometric Optics for Surface Waves in Nonlinear Elasticity.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c1920.
264		4	_c©1920.
300			_a1 online resource (164 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society Series ; _vv.263
505	0		_aCover -- 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			_aThis 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			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aPartial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations.
655		4	_aElectronic books.
700	1		_aWilliams, Mark.
776	0	8	_iPrint version: _aCoulombel, Jean-François _tGeometric Optics for Surface Waves in Nonlinear Elasticity _dProvidence : American Mathematical Society,c1920 _z9781470440374
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society Series
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6176743 _zClick to View
999			_c17670 _d17670