Blow-Up of Solution to Cauchy Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation

Abstract

We consider the singularly perturbed sixth-order Boussinesq-type equation, which describes the bidirectional propagation of small amplitude and long capillary gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to 1/3. The sufficient conditions of blow-up of solution to the Cauchy problem for this equation are given.

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Song, C. and Chen, L. (2015) Blow-Up of Solution to Cauchy Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation. Journal of Applied Mathematics and Physics, 3, 834-838. doi: 10.4236/jamp.2015.37103.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Song, C., Li, H. and Li, J. (2013) Initial Boundary Value Problem for the Singularly Perturbed Boussinesq-Type Equation. Discrete and Continuous Dynamical Systems, 709-717.
[2] Song, C., Li, J. and Gao, R. (2014) Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq Equation. Hindawi Publishing Corporation Journal of Applied Mathematics.
[3] Becken, E.F. and Bellman, R. (1983) Inequalities (Fourth Printing). Springer-Verlag, Berlin.
[4] Y D. (1989) L2 Theory of Partial Differential Equations. Peking University Press, Beijing. (In Chinese)

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