Skip to main content

Problemes Mixtes Hyperboliques

  • Chapter
Hyperbolicity

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 72))

  • 924 Accesses

Résumé

Ce texte est compose dé deux parties assez independantes.

La première partie. concerne l’existence et l’unicité des solutions; le point essentiel réside dans la démonstration de l’inegalite d’énergie pour les problèmes mixtes.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.95
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

References Pour La 1ère Partie

  • M.S. AGRANOVITCH Boundary value problems for systems with a pararnetor Mat. Sbornik, Tom 84 (126) (1971) no 1 Math. USSR Sbornik, Vol 13 (1971), no 1

    Google Scholar 

  • K.D. FRIEDRICHS, P.D. LAX On symmetrizable differential operators Proceedings of Symposia in Pure Math., Vol. 10

    Google Scholar 

  • R. Hersh Mixed problems in several variables Journal of Mathematics and Mechanics, Vol. 12, no 3 (1963), p. 317–334

    MathSciNet  MATH  Google Scholar 

  • H.O. Kreiss Initial boundary value problems for hyperbolic systems Comm. Pure Appi. Math., Vol 23 (1970), p. 277–298

    Article  MathSciNet  Google Scholar 

  • J. Ralston Note on a paper of Kreiss Comm. Pure Appi. Math., Vol 24, (1971), p. 759–762

    Article  MathSciNet  Google Scholar 

  • J. RAUCH L2 is a continuable initial condition of Kreiss’ mixed problems Comm. Pure Appi. Math., Vol 25 (1972), p. 265–285

    Article  MathSciNet  MATH  Google Scholar 

  • R. Sakamoto Mixed problems for hyperbolic equations I and II Journ. Math. Kyoto Univ., 10 (1970), p. 375–401 and 403–417bl]References Pour La 2ème-Partie

    Google Scholar 

References Pour La 2ère Partie

  • J. CHAZARAIN [ 1 ] Paramétrix du problème mixte pour l’équation des ondes à l’intérieur d’un domaine convexe pour les bicaractéristiques. Astérisque no 34–35 (1976) Journées Equations aux Dérivées Partielles de Rennes

    Google Scholar 

  • J. CHAZARAIN [ 2 ] Reflection of singularities for a class of operators with multiple characteristics. A paraître dans Publ. RIMS Kyoto Univ. (1976)

    Google Scholar 

  • J.J. DUISTERMAAT Fourier Integral Operators. Lecture Notes, Courant Institute N.Y. U (1973)

    Google Scholar 

  • G.I. ESKIN The Cauchy problem for hyperbolic systems in convolutions trad. Math. USSR — Sbornik 3 (1967) 243–277

    Google Scholar 

  • L. HORMANDER [ 1 ] Pseudo-differential operators and hypoelliptic equations A.M.S. Symp. Pure Math 10 (1966) 138–183

    Google Scholar 

  • L. HORMANDER [ 2 ] The spectral function of an elliptic operator. Acta Math 121 (1968) 193–218

    Google Scholar 

  • L. HORMANDER [ 3 ] The Calculus of Fourier Integral Operators. Conference on Prospects in Mathematics, Princeton Univ. Press (1971)

    Google Scholar 

  • L. HORMANDER [ 4 ] Linear Differential Operators. Actes du Congrès International des Mathématiciens, Nice (1970) Tome 1 p. 121–133

    Google Scholar 

  • L. HORMANDER [ 5 ] Fourier Integral Operators I. Acta Math. (1971), 79–183

    Google Scholar 

  • M.V. FEDORYUK The stationary phase method and pseudo-differential operators. Trad. Russian Math Survey 26 no 1 (1971) 65–115

    Google Scholar 

  • H. KUMANO-GO Remarks on pseudo-differential operators. J. Math. Soc. Japan 21 (1969) 413–439

    Google Scholar 

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

    Google Scholar 

  • R.B. MELROSE Microlocal parametrices for diffractive boundary value prolblems. Duke Math. J. 42 (1975) 605–635

    Google Scholar 

  • L. NIRENBERG [ 1 ] Pseudo differential operators. A.M.S. Symp. Pure Math. 16 (1970) 149–167

    Google Scholar 

  • L. NIRENBERG [ 2 ] Lectures on Linear partial differential equations. Regional Conf. Series in Math. No 17 A.M.S. (1973)

    Google Scholar 

  • M. TAYLOR Grazing rays and reflection of singularities of solutions to wave equations. C.P.A.M. 39 (1976) 1–38

    Google Scholar 

  • F. TREVES Basic Linear Partial Differential Equations. Acad. Press (1975)

    Google Scholar 

Download references

Authors

Editor information

Giuseppe Da Prato Giuseppe Geymonat

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Chazarain, J., Piriou, A. (2011). Problemes Mixtes Hyperboliques. In: Da Prato, G., Geymonat, G. (eds) Hyperbolicity. C.I.M.E. Summer Schools, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11105-1_2

Download citation

Publish with us

Policies and ethics