Skip to main content

On the Ill-posed Hyperbolic Systems with a Multiplicity Change Point of Not Less Than the Third Order

  • Chapter
Recent Trends in Toeplitz and Pseudodifferential Operators

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 210))

  • 577 Accesses

Abstract

Hyperbolic systems with noninvolutive multiple characteristics are considered and an example of ill-posed Cauchy problem is proposed.

This research was partially supported by project of CONACYT Mexico and by project of SIP - IPN.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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. A.V. Krivko, V.V. Kucherenko, On Real Hyperbolic Systems with Characteristics of Variable Multiplicity Doklady Mathematics 75, N.1 (2007), 83–86

    Article  Google Scholar 

  2. V.V. Kucherenko, Asymptotics of the solution of the system A(x,-ih∂/∂x) as h → 0 in the case of characteristics of variable multiplicity Izv. AN SSSR. Ser. Mat. 38 (3) (1974) 625–662

    Google Scholar 

  3. V.Ya. Ivrii, and V.M. Petkov, Necessary conditions for the Cauchy problem for nonstrictly hyperbolic equations to be well posed Russ. Math. Surv. 29 (5) (1974) 3–70

    Article  MathSciNet  Google Scholar 

  4. R.B. Melrose and G.A. Uhlmann, Lagrangian intersection and the Cauchy problem Comm. Pure Appl. Math. 32 (1979) 483–519

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Kryvko and V.V. Kucherenko, Stability of stationary solutions of nonlinear hyperbolic systems with multiple characteristics Proceedings of ISAAC Congress 2005 (2009)

    Google Scholar 

  6. V.P. Maslov, Perturbation Theory and Asymptotic Methods Izdat. Moskov. Gos. Univ., Moscow, 1965 (Dunod, Paris, 1972)

    Google Scholar 

  7. V.P. Maslov and M.V. Fedoruk, Semi-Classical Approximation in Quantum Mechanics Nauka, Moscow,1976 (Reidel, Dordrecht, 1981)

    Google Scholar 

  8. L. Hörmander, The Analysis of Linear Partial Differential Operators, II Springer Verlag, Berlin, 1983

    MATH  Google Scholar 

  9. V.V. Kucherenko and Yu. Osipov, The Cauchy problem for nonstrictly hyperbolic equations Math. USSR Sbornik 48(1) (1984) 81–109

    Article  MATH  Google Scholar 

  10. H. Flaschka and G. Strang, The correctness of the Cauchy problem Advances in Math. 6(3) (1971) 347–379

    Article  MATH  MathSciNet  Google Scholar 

  11. R. Courant and D. Hilbert, Methods of Mathematical Physics John Wiley and Sons, New York, 1962

    MATH  Google Scholar 

  12. M.V. Karasev, Weyl and ordered calculus of noncommuting operators Math. Notes 26(6) (1979) 885–907

    MathSciNet  Google Scholar 

  13. M.V. Karasev and V.P. Maslov, Nonlinear Poisson Brackets Geometry and Quantization AMS, 1993

    Google Scholar 

  14. M.V. Fedoruk, Metod Perevala Nauka, Moscow, 1977

    Google Scholar 

  15. S.Yu. Dobrokhotov, Resonances in multi-frequency averaging theory of nonlinear partial differential equations Singular limits of dispersive waves, NATO ASI Series, Ser. B, 320 (1994) 203–217

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to 60th birthday of Nikolai Vasilevski

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Basel AG

About this chapter

Cite this chapter

Kucherenko, V.V., Kryvko, A. (2010). On the Ill-posed Hyperbolic Systems with a Multiplicity Change Point of Not Less Than the Third Order. In: Duduchava, R., Gohberg, I., Grudsky, S.M., Rabinovich, V. (eds) Recent Trends in Toeplitz and Pseudodifferential Operators. Operator Theory: Advances and Applications, vol 210. Springer, Basel. https://doi.org/10.1007/978-3-0346-0548-9_8

Download citation

Publish with us

Policies and ethics