{"paper":{"title":"Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changjiang Zhu, Haibo Cui, Haiyan Yin, Limei Zhu","submitted_at":"2017-08-30T05:40:35Z","abstract_excerpt":"This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\\in \\mathbb{R}^+\\times\\mathbb{R}^+$, \\begin{equation}\\notag \\partial_t v\n  -\n  \\partial_x u=0, \\qquad \\partial_t u\n  +\n  \\partial_x p(v)\n  =\\displaystyle\n  -\\frac{\\alpha}{(1+t)^\\lambda} u, \\end{equation} with null-Dirichlet boundary condition or null-Neumann boundary condition on $u$. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends time-asymptotically to the nonlinear diffusion wave. Compared w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09127","kind":"arxiv","version":1},"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"}