A spectral study of an infinite axisymmetric elastic layer

Chorfi, Lahcène

doi:10.1051/m2an:2001138

Search citation statements

Order By: Relevance

Paper Sections

Select...

Axisymmetric Green Function1

The Integral Formulation1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2006

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This can be seen if we write the equation * u + 2 u = 0 in cylindrical co-ordinates and consider the axisymmetric solution u(r, z) = u 1 (r, z)e r +u 3 (r, z)e z (see Reference [18]). Moreover, we have:…”

Section: Axisymmetric Green Functionmentioning

confidence: 99%

See 1 more Smart Citation

Solvability of singular integral system connected with seismic waves around the borehole

Alem

Chorfi

2006

Math. Meth. Appl. Sci.

Self Cite

View full text Add to dashboard Cite

SUMMARYWe study in this article a boundary-value problem arising in the propagation of waves in an elastic half-space covered by a layer with a vertical borehole. We first show a uniqueness theorem under some restrictions on the solution. For the existence, we use the direct integral equation method. We obtain a singular integral system on the half-line. For the solvability, we reduce this system to an elliptic pseudodifferential equation and establish the Fredholm property. Finally, we compute the index of the associated operator for various values of Poisson's ratio.

show abstract

Section: Axisymmetric Green Functionmentioning

confidence: 99%

“…and u 3 (r, 0) = C 3 e ik s r r + O 1 r 3/2 (18) according to Abel criterium. Then we have proved the following theorem.…”

Section: The Integral Formulationmentioning

confidence: 99%