Lower regularity solutions of non-homogeneous boundary value problems of the sixth order Boussinesq equation in a quarter plane

2018/11/14 by Li, Shenghao, Chen, Min, Zhang, Bingyu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.05914

Abstract

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-u_xxxxxx+(u²)_xx=0, xgt;0, tgt;0, u(x,0)=φ(x), u_t(x,0)=ψ''(x), u(0,t)=h₁(t), u_xx(0,t)=h₂(t), u_xxxx(0,t)=h₃(t), where β=±1. It is shown that the problem is locally well-posed in H^s(ℝ⁺) for -\frac12

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