Generalized linear elasticity in exterior domains. I: Radiation problems

Weck, Norbert; Witsch, Karl‐Josef

doi:10.1002/(sici)1099-1476(19971125)20:17<1469::aid-mma935>3.0.co;2-l

Cited by 17 publications

(18 citation statements)

References 21 publications

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“…(N-corr) (Here " · " Q : """ · "" Q in the notation of [17].) Our results may be shortly described as follows:…”

Section: More Precisely With T'2k#2!n/2 S'2k#mentioning

confidence: 89%

“…Thus in all sections but the last we use (A ) as a general assumption. Furthermore, we shall always use [17,Ch. 5,Assumptions 1#2].…”

Section: More Precisely With T'2k#2!n/2 S'2k#mentioning

confidence: 99%

“…I , f ! I as defined by (9), (10), (16), (17) will be called solutions of (2) of 'type' 1, 2 , 4 (in this order).…”

Section: Towers Of Special Solutions In Elasticitymentioning

confidence: 99%

“…(We use 1 , 2 instead of 1 , 2 as in [17] because there is no need to distinguish different scalar products.) We obtain…”

Section: Towers Of Special Solutions In Elasticitymentioning

confidence: 99%

“…We continue the study of the operator E of Part I [17]. Now, we look upon boundary value problems for E and E!…”

Section: Introductionmentioning

confidence: 99%

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Generalized linear elasticity in exterior domains. II: low-frequency asymptotics

Weck

Witsch

1997

Math. Meth. Appl. Sci.

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We continue the study of the operators of generalized linear elasticity and investigate the behaviour of the solutions as the frequency tends to zero. We identify degenerate operators in terms of special solutions to the static problem which must be added to the usual Neumann series in order to describe the low frequency behaviour adequately. As a byproduct we construct solutions to the homogeneous static operator (‘spherical elastics’) which generalize the spherical harmonics and give rise to a ‘spherical elastics expansion’. © 1997 B. G. Teubner Stuttgart‐John Wiley & Sons Ltd.

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“…(N-corr) (Here " · " Q : """ · "" Q in the notation of [17].) Our results may be shortly described as follows:…”

Section: More Precisely With T'2k#2!n/2 S'2k#mentioning

confidence: 89%

“…Thus in all sections but the last we use (A ) as a general assumption. Furthermore, we shall always use [17,Ch. 5,Assumptions 1#2].…”

Section: More Precisely With T'2k#2!n/2 S'2k#mentioning

confidence: 99%

“…I , f ! I as defined by (9), (10), (16), (17) will be called solutions of (2) of 'type' 1, 2 , 4 (in this order).…”

Section: Towers Of Special Solutions In Elasticitymentioning

confidence: 99%

“…(We use 1 , 2 instead of 1 , 2 as in [17] because there is no need to distinguish different scalar products.) We obtain…”

Section: Towers Of Special Solutions In Elasticitymentioning

confidence: 99%

“…We continue the study of the operator E of Part I [17]. Now, we look upon boundary value problems for E and E!…”

Section: Introductionmentioning

confidence: 99%

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Generalized linear elasticity in exterior domains. II: low-frequency asymptotics

Weck

Witsch

1997

Math. Meth. Appl. Sci.

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Unique continuation for systems with Lamé principal part

Weck

2001

Math Methods in App Sciences

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The scattering theory of C. Wilcox in elasticity

Mabrouk¹,

Helali

2002

Math Methods in App Sciences

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SUMMARYWe extend the abstract time-dependent scattering theory of C.H. Wilcox to the case of elastic waves. Most of the results are proved with the minimal assumption that the obstacle satisÿes the energy local compactness condition (ELC Notations: Let us ÿrst explain the notations which are used throughout the text. The space R 3 is endowed with the canonical basis {e 1 ; e 2 ; e 3 }, the origin O and the coordinate system (x 1 ; x 2 ; x 3 ). The canonical scalar product of R 3 is denoted by a dot. By a '·' we mean the contracted product of tensors. Vectors and matrices are typed in bold style.I is the identity map or matrix or tensor. When we want more precision, we use the notation id X for the identity map in the space X . For a matrix or a map A; t A means the transpose. For any open set ⊆ R 3 , we introduce the classical spaces of scalar complex functions: 3 . * = − curlcurl + ( + ) graddiv is the LamÃ e operator, ; are the LamÃ e constants, c 1 = + 2 ; c 2 = √ are the speeds of the longitudinal and shear waves and we set c jl = c j =c l ; k j (!) = c j =! are wave numbers. T(u; n) = 2 (9u=9n) + n div u + n ∧ curl u is the traction vector at the boundary point where the normal is n.

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Generalized linear elasticity in exterior domains. I: Radiation problems

Cited by 17 publications

References 21 publications

Generalized linear elasticity in exterior domains. II: low-frequency asymptotics

Generalized linear elasticity in exterior domains. II: low-frequency asymptotics

Unique continuation for systems with Lamé principal part

The scattering theory of C. Wilcox in elasticity

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