Skip to main content

Singularities in linear wave propagation

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((2803,volume 1241))

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.95
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Huygens C. Abhandlung über das Licht. Ostwalds Klassiker 20(1913)

    Google Scholar 

  • Fresnel A.J. Ouevres complètes (1866–70). Imprimerie Impériale Paris.

    Google Scholar 

  • Lame G. Leçons sur la théorie mathématique de l'elasticité des corps solides. Deuxième edition (1866), Paris, Gauthier-Villars.

    Google Scholar 

  • Kovalevsky S.V. Über die Brechung des Lichtes in cristallischen Mitteln. Acta Math. 6 (1985)249–304

    Google Scholar 

  • Tedone O. Sull'integrazione dell'equazione... Ann. di Mat. Ser. 3 vol. 1 (1889)

    MATH  Google Scholar 

  • Volterra V. Sur les vibrations lumineuses dans le milieux biréfringents. Acta Math. 16(1892)154–21

    Article  MathSciNet  Google Scholar 

  • Zeilon N. Sur les équations aux dérivées partielles à quatre dimensions et le problème optique des milieux biréfringents I,II. Acta Reg. Soc. Sc. Upsaliensis Ser. IV vol.5 No 3 (1919), 1–57 and No 4(1921), 1–130

    MATH  Google Scholar 

  • Hadamard J. Le problème de Cauchy et les équations aux derivées partielles hyperboliques. Hermann et Cie, Paris 1932. (Originally lectures at Yale Univ. 1922)

    Google Scholar 

  • Herglotz G. Über die Integration linearer partieller Differentialglechungen mit konstanten Koeffizienten. Ber. Sächs. Akad. Wiss, 78 (1926), 93–126, 287–318, 80 (1928)69–114

    Google Scholar 

  • Petrovsky I.G. Über das Cauchysche Probelm fur Systeme von partiellen Differentalgleichungen. Mat. Sb. 2(44) (1937)815–870

    Google Scholar 

  • — On the diffusion of waves and lacunas for hyperbolic equations. Mat. Sb. 17(59) (1945)145–215

    MathSciNet  Google Scholar 

  • Riesz M. L'intégrale de Riemann-Liouville et le problème de Cauchy. Acta Math 81 (1949) 1–223.

    Article  MathSciNet  MATH  Google Scholar 

  • Gårding L. Solution directe du problème de Cauchy pour les équations hyperboliques. Coll. Int. CNRS Nancy 1956, 71–90

    Google Scholar 

  • Lax P. Asymptotic solutions of oscillatory initial value problems. Duke Math. J. 24 (1957) 627–646

    Article  MathSciNet  MATH  Google Scholar 

  • Ludwig G. Conical refraction in Crystal Optics and Hydromagnetics. Comm. Pure Appl Math XIV (1961)113–124

    Google Scholar 

  • Duistermaat J.J. and Hörmander L. Fourier integral operators II. Acta Math. 128 (1972) 183–269

    Article  MathSciNet  MATH  Google Scholar 

  • Atiyah M.F., Bott R., Gårding L. Lacunas for hyperbolic differential operators with constant coefficients I,II. Acta Math. 124(1970),109–189 and 131(1973)145–206

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this chapter

Cite this chapter

Gårding, L. (1987). Singularities in linear wave propagation. In: Singularities in Linear Wave Propagation. Lecture Notes in Mathematics, vol 1241. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073089

Download citation

  • DOI: https://doi.org/10.1007/BFb0073089

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18001-2

  • Online ISBN: 978-3-540-47216-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics