{"paper":{"title":"Interaction between nonlinear diffusion and geometry of domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2010-09-30T13:49:55Z","abstract_excerpt":"Let $\\Omega$ be a domain in $\\mathbb R^N$, where $N \\ge 2$ and $\\partial\\Omega$ is not necessarily bounded. We consider nonlinear diffusion equations of the form $\\partial_t u= \\Delta \\phi(u)$. Let $u=u(x,t)$ be the solution of either the initial-boundary value problem over $\\Omega$, where the initial value equals zero and the boundary value equals 1, or the Cauchy problem where the initial data is the characteristic function of the set $\\mathbb R^N\\setminus \\Omega$.\n  We consider an open ball $B$ in $\\Omega$ whose closure intersects $\\partial\\Omega$ only at one point, and we derive asymptotic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6131","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"}