{"paper":{"title":"Lower regularity solutions of non-homogeneous boundary value problems of the sixth order Boussinesq equation in a quarter plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bingyu Zhang, Min Chen, Shenghao Li","submitted_at":"2018-11-14T17:18:26Z","abstract_excerpt":"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}+\\beta u_{xxxx}-u_{xxxxxx}+(u^2)_{xx}=0,\\quad x>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 $(\\varphi,\\psi)\\in H^s(\\mathbb{R}^+)\\times H^{s-1}(\\mathbb{R}^+)$ and boundary condition $(h_1,h_2,h_3) $ in the prod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05914","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}