Skip to main content

Mathematics and the Trajectories of Typhoons

  • Chapter
Mathematical Events of the Twentieth Century
  • 1834 Accesses

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. V. P. Maslov. Three algebras corresponding to nonsmooth solutions of systems of quasi-linear hyperbolic equations. Uspekhi Mat. Nauk, 1980, 35(2), 252–253 (Russian).

    Google Scholar 

  2. V. P. Maslov. On the propagation of a shock wave in an isoentropic nonviscous gas. In: Itogi Nauki i Tekhniki VINITI, T. 8. Moscow: VINITI, 1977, 199–271 (Russian).

    Google Scholar 

  3. J. F. Colombeau. Elementary Introduction to New Generalized Functions. Amsterdam: North-Holland, 1985.

    MATH  Google Scholar 

  4. Yu.V. Egorov. A contribution to the theory of generalized functions. Russ. Math. Surveys, 1990, 45(5), 1–49.

    Article  MATH  Google Scholar 

  5. V.G. Danilov, V. P. Maslov, V.M. Shelkovich. Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems. Theor. Math. Phys., 1998, 114(1), 1–42.

    MATH  MathSciNet  Google Scholar 

  6. S.Yu. Dobrokhotov, K.V. Pankrashkin, E. S. Semenov. Proof of Maslov’s conjecture about the structure of weak point singular solution of the shallow water equations. Russ. J. Math. Phys., 2001, 8(1), 25–52.

    MATH  MathSciNet  Google Scholar 

  7. S.Yu. Dobrokhotov. Hugoniot-Maslov chains for solitary vortices of the shallow water equations, I; II. Russ. J. Math. Phys., 1999, 6(2), 137–173; 6(3), 282–313.

    MATH  MathSciNet  Google Scholar 

  8. S.Yu. Dobrokhotov. Integrability of truncated Hugoniot-Maslov chains for trajectories of mesoscale vortices on shallow water. Theor. Math. Phys., 2000, 125(3), 1721–1741.

    Article  MATH  MathSciNet  Google Scholar 

  9. V. P. Maslov, G.A. Omel’yanov. Hugoniot-type conditions for infinitely narrow solutions of the equations for simple waves. Sib. Math. J., 1983, 24(5), 787–795.

    Article  MATH  MathSciNet  Google Scholar 

  10. A.M. Obukhov. On the problem of geostrophic wind. Izv. Akad. Nauk SSSR. Ser. Geogr., 1949, 13(4), 281–306 (Russian).

    Google Scholar 

  11. F.V. Dolzhanskii, V.A. Krymov, D.Yu. Manin. Stability and vortex structures of quasi-two-dimensional shear flows. Physics-Uspekhi, 1990, 33(7), 495–520.

    Article  Google Scholar 

  12. J. Pedlosky. Geophysical Fluid Dynamics, 2nd edition. New York: Springer, 1987.

    MATH  Google Scholar 

  13. V.V. Bulatov, Yu.V. Vladimirov, V.G. Danilov, S.Yu. Dobrokhotov. An example of computation of the “eye” of a typhoon on the basis of Maslov’s conjecture. Dokl. Ross. Akad. Nauk, 1994, 338(1), 102–105 (Russian).

    MATH  MathSciNet  Google Scholar 

  14. S.Yu. Dobrokhotov, B. Tirozzi. On the Hamiltonian property of the truncated Hugoniot-Maslov chain for trajectories of mesoscale vortices. Russ. Acad. Sci. Dokl. Math., 2002, 65(3), 453–458.

    Google Scholar 

  15. S.Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi. Hugoniot-Maslov chains for singular vorticial solutions to quasilinear hyperbolic systems and typhoon trajectory. J. Math. Sci., 2004, 124(5), 5209–5249.

    Article  MathSciNet  Google Scholar 

  16. R. Ravindran, P. Prasad. A new theory of shock dynamics, I; II. Appl. Math. Letters, 1990, 3(2), 77–81; 3(3), 107–109.

    Article  MATH  MathSciNet  Google Scholar 

  17. S.Yu. Dobrokhotov, E. S. Semenov, B. Tirozzi. Calculation of the integrals of the Hugoniot-Maslov chains for singular vortex solutions of shallow water equation. Theor. Math. Phys., 2004, 139(1), 500–512.

    Article  MathSciNet  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Maslov, V.P. (2006). Mathematics and the Trajectories of Typhoons. In: Bolibruch, †.A.A., et al. Mathematical Events of the Twentieth Century. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-29462-7_9

Download citation

Publish with us

Policies and ethics