Skip to main content

Singularities of the Reflected and Refracted Riemann Functions of Elastic Wave Propagation Problems in Stratified Media

  • Chapter
Direct and Inverse Problems of Mathematical Physics

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 5))

  • 819 Accesses

Abstract

In this paper we shall study elastic mixed or initial-interface value problems and give an inner estimate of the location of singularities of the reflected and refracted Riemann functions by making use of the localization method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. F. Atiyah, R. Bott, L. Girding, Lacunas for hyperbolic differential operators with constant coefficients I, Acta Math. 124 (1970), 109–189.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Matsumura, Localization theorem in hyperbolic mixed problems, Proc. Japan. Acad. 47 (1971), 115–119.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Matsumura, On the singularities of the Riemann functions of mixed problems for the wave equation in plane-stratified media I, Proc. Japan. Acad. 52 (1976), 289–292.

    Article  MathSciNet  Google Scholar 

  4. M. Matsumura, On the singularities of the Riemann functions of mixed problems for the wave equation in plane-stratified media II, Proc. Japan. Acad. 52 (1976), 293–295.

    Article  MathSciNet  Google Scholar 

  5. S. Shimizu, Eigenfunction expansions for elastic wave propagation problems in stratified media R3, Tsukuba J. Math. 18 (1994), 283–350.

    MathSciNet  MATH  Google Scholar 

  6. M. Tsuji, Propagation of the singularities for hyperbolic equations with constant coefficients, Japan J. Math. 2 (1976), 369–373.

    MathSciNet  Google Scholar 

  7. S. Wakabayashi, Singularities of the Riemann functions of hyperbolic mixed problems in a quater-space, Proc. Japan. Acad. 50 (1974), 821–825.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Wakabayashi, Singularities of the Riemann functions of hyperbolic mixed problems in a quater-space, Publ. RIMS Kyoto Univ. 11 (1976), 785–807.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Shimizu, S. (2000). Singularities of the Reflected and Refracted Riemann Functions of Elastic Wave Propagation Problems in Stratified Media. In: Gilbert, R.P., Kajiwara, J., Xu, Y.S. (eds) Direct and Inverse Problems of Mathematical Physics. International Society for Analysis, Applications and Computation, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3214-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-3214-6_21

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4818-2

  • Online ISBN: 978-1-4757-3214-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics