Skip to main content

Global Weak Solutions for a Shallow Water Equation

  • Conference paper
Hyperbolic Problems: Theory, Numerics, Applications

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
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. Camassa, R., Holm, D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71, 1661–1664 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  2. Coclite, G.M., Holden, H., Karlsen, K.H.: Global weak solutions to a generalized hyperelastic-rod wave equation. SIAM J. Math. Anal., 37, 1044–1069 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  3. Coclite, G.M., Holden, H., Karlsen, K.H.: Wellposedness for a parabolic-elliptic system. Discrete Contin. Dyn. Syst., 13, 659–682 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  4. Constantin, A., Escher, J.: Global weak solutions for a shallow water equation. Indiana Univ. Math. J., 47, 1527–1545 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  5. Constantin, A., Molinet, L.: Global weak solutions for a shallow water equation. Comm. Math. Phys., 211, 45–61 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  6. Danchin, R.: A few remarks on the Camassa–Holm equation. Differential Integral Equations, 14, 953–988 (2001).

    MATH  MathSciNet  Google Scholar 

  7. Danchin, R.: A note on well-posedness for Camassa–Holm equation. J. Differential Equations, 192, 429–444 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  8. Dullin, H., Gottwald, G., Holm, D.: An integrable shallow water equation with linear and nonlinear dispersion. Phy. Rev. Lett., 87, 194501 (2001).

    Article  Google Scholar 

  9. Johnson, R.S.: Camassa–Holm, Korteweg–de Vries and related models for water waves. J. Fluid Mech., 455, 63–82 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  10. Lieb, E.H., Loss, M.: Analysis. American Mathematical Society, Providence, RI, second edition (2001).

    MATH  Google Scholar 

  11. Liu, Y.: Global existence and blow-up solutions for a nonlinear shallow water equation. Math. Ann., 335, 717–735 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  12. Oleuınik, O.A.: Discontinuous solutions of non-linear differential equations. Amer. Math. Soc. Transl. Ser. 2, 26, 95–172 (1963).

    Google Scholar 

  13. Simon, J.: Compact sets in the space L p(0,T; B). Ann. Mat. Pura Appl., 146, 65–96 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  14. Xin, Z., Zhang, P.: On the weak solutions to a shallow water equation. Comm. Pure Appl. Math., 53, 1411–1433 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  15. Xin, Z., Zhang, P.: On the uniqueness and large time behavior of the weak solutions to a shallow water equation. Comm. Partial Differential Equations, 27, 1815–1844 (2002).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coclite, G.M., Holden, H., Karlsen, K.H. (2008). Global Weak Solutions for a Shallow Water Equation. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_35

Download citation

Publish with us

Policies and ethics