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math.AP2018
Hexagonal standing wave patterns of a two-dimensional Boussinesq system
Shenghao Li, Min Chen, Bing-Yu Zhang
We prove the existence of a large family of two-dimensional standing waves, that are triple periodic solutions, for a Boussinesq system which describes two-way propagation of water…
math.AP2018
Exact controllability and stability of the Sixth Order Boussinesq equation
Shenghao Li, Min Chen, Bing-Yu Zhang
The article studies the exact controllability and the stability of the sixth order Boussinesq equation \[ u_{tt}-u_{xx}+βu_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=f, \quad β=\pm1, \] on the i…
math.AP2018
Lower regularity solutions of non-homogeneous boundary value problems of the sixth order Boussinesq equation in a quarter plane
Shenghao Li, Min Chen, Bingyu Zhang
In this article, we study an initial-boundary-value problem of the sixth order Boussinesq equation on a half line with nonhomogeneous boundary conditions: \[ u_{tt}-u_{xx}+βu_{xxxx…