{"paper":{"title":"Asymptotic analysis for Cahn--Hilliard type phase field systems related to tumor growth in general domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shunsuke Kurima","submitted_at":"2018-08-11T08:11:07Z","abstract_excerpt":"This article considers a limit system by passing to the limit in the following Cahn--Hilliard type phase field system related to tumor growth as $\\beta\\searrow0$:\n  \\begin{equation*}\n  \\begin{cases}\n  \\alpha\\partial_{t} \\mu_{\\beta} + \\partial_{t} \\varphi_{\\beta}-\\Delta\\mu_{\\beta} = p(\\sigma_{\\beta} - \\mu_{\\beta}) & \\mbox{in}\\ \\Omega\\times(0, T),\n  \\\\[1mm]\n  \\mu_{\\beta} = \\beta\\partial_{t} \\varphi_{\\beta} + (-\\Delta+1)\\varphi_{\\beta} + \\xi_{\\beta} + \\pi(\\varphi_{\\beta}),\\ \\xi_{\\beta} \\in B(\\varphi_{\\beta})\n  & \\mbox{in}\\ \\Omega\\times(0, T),\n  \\\\[1mm]\n  \\partial_{t} \\sigma_{\\beta} -\\Delta\\sigma_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03771","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"}