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Global Weak Solutions for a Shallow Water Equation

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Hyperbolic Problems: Theory, Numerics, Applications

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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 

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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

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