{"paper":{"title":"Non-dissipative system as limit of a dissipative one: comparison of the asymptotic regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ricardo P. Silva","submitted_at":"2018-10-06T21:00:33Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^n$ be a bounded smooth domain (open and connected) in $\\mathbb{R}^n$. Given $u_0\\in L^2(\\Omega)$, $g\\in L^\\infty(\\Omega)$ and $\\lambda \\in \\mathbb{R}$, our purpose is to describe the asymptotic behavior of weak solutions of the family of problems \\begin{equation*} \\left\\{ \\begin{array}{rcll} \\dfrac{\\partial u}{\\partial t} - \\Delta_p u & = & \\lambda u + g, & \\text{ on } \\quad (0,\\infty)\\times \\Omega, \\\\ u & = & 0, & \\text{ in } \\quad (0,\\infty)\\times \\partial \\Omega, \\\\ u(0, \\cdot) & = & u_0, & \\text{ on } \\quad\\Omega, \\end{array} \\right. \\end{equation*} as $p \\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03054","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"}