Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (6): 1552-1567.

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Cauchy Problem for a Generalized System of Coupled Boussinesq Type Equations Arising from Nonlinear Layered Lattice Model

Xiangying Chen1,*(),Guowang Chen2()   

  1. 1 Common Teaching Department, Zhengzhou Electric Power College, Zhengzhou 450000
    2 School of Mathematics and Satistics, Zhengzhou University, Zhengzhou 450052
  • Received:2019-10-25 Online:2020-12-26 Published:2020-12-29
  • Contact: Xiangying Chen;
  • Supported by:
    the NSFC(11671367);the NSFC(11171311)


In this paper, we prove that the Cauchy problem for a generalized system of the coupled Boussinesq-type equations arising from nonlinear layered lattice model has a unique global generalized solution in $C([0, \infty);H^s(\ {\Bbb R})\times H^s(\ {\Bbb R}))(s\geq2$ is a real number) and a unique global classical solution in $C^2([0, \infty);C_B^2(\ {\Bbb R})\times C_B^2(\ {\Bbb R}))(s>\frac{5}{2})$. The sufficient conditions for the blow up of the solution to the Cauchy problem above are given.

Key words: Generalized system of coupled Boussinesq-type equations, Cauchy problem, Global solution, Blow up of solution

CLC Number: 

  • O175.2