English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we study an initial-boundary-value problem of the sixthorder Boussinesq equation on a half line with nonhomogeneous boundaryconditions: \[ u_{tt}-u_{xx}+\beta u_{xxxx}-u_{}+(u^2)_{xx}=0,\quadx>0\mbox{, }t>0,\] \[u(x,0)=\varphi (x), u_t(x,0)=\psi ''(x),\] \[u(0,t)=h_1(t), u_{xx}(0,t)=h_2(t), u_{xxxx}(0,t)=h_3(t),\] where $\beta=\pm1$.It is shown that the problem is locally well-posed in $H^s(\mathbb{R}^+)$ for$-\frac12<s\leq 0$ with initial condition $(\varphi,\psi)\inH^s(\mathbb{R}^+)\times H^{s-1}(\mathbb{R}^+)$ and boundary condition$(h_1,h_2,h_3) $ in the product space $H^{\frac{s+1}{3}}(\mathbb{R}^+)\timesH^{\frac{s-1}{3}}(\mathbb{R}^+)\times H^{\frac{s-3}{3}}(\mathbb{R}^+)$.

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