25 citations · 127 across the 20 of their papers we have counts for
20 papers
Lower Regularity Solutions of the Non-homogeneous Boundary-Value Problem for a Higher Order Boussinesq Equation in a Quarter Plane
Shenghao Li, Min Chen, Xin Yang +1
We continue to study the initial-boundary-value problem of the sixth order Boussinesq equation in a quarter plane with non-homogeneous boundary conditions: \begin{equation*} \begin…
Well-posedness and Critical Index Set of the Cauchy Problem for the Coupled KdV-KdV Systems on
Xin Yang, Bing-Yu Zhang
Studied in this paper is the well-posedness of the Cauchy problem for the coupled KdV-KdV systems \[ u_t+a_1u_{xxx} = c_{11}uu_x+c_{12}vv_x+d_{11}u_{x}v+d_{12}uv_{x}, \quad u(x,0)=…
Local Exact Controllability to the Trajectories of the Korteweg-de Vries-Burgers Equation on a Bounded Domain with Mixed Boundary Conditions
Eduardo Cerpa, Cristhian Montoya, Bingyu Zhang
This paper studies the internal control of the Korteweg-de Vries-Burgers (KdVB) equation on a bounded domain. The diffusion coefficient is time-dependent and the boundary condition…
Local Well-posedness of the Coupled KdV-KdV Systems on
Xin Yang, Bing-Yu Zhang
Inspired by the recent successful completion of the study of the well-posedness theory for the Cauchy problem of the Korteweg-de Vries (KdV) equation \[ u_t +uu_x +u_{xxx}=0, \quad…
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…
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…