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On the Cauchy Problem for a Class of Weakly Dissipative One-Dimensional Shallow Water Equations

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  • Jingjing Xu
  • Zaihong Jiang

Abstract

We investigate a more general family of one-dimensional shallow water equations with a weakly dissipative term. First, we establish blow-up criteria for this family of equations. Then, global existence of the solution is also proved. Finally, we discuss the infinite propagation speed of this family of equations.

Suggested Citation

  • Jingjing Xu & Zaihong Jiang, 2013. "On the Cauchy Problem for a Class of Weakly Dissipative One-Dimensional Shallow Water Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, October.
    • Handle: RePEc:hin:jnlaaa:851476
    DOI: 10.1155/2013/851476
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