{"paper":{"title":"Boundary value problem for a classical semilinear parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Ma","submitted_at":"2010-12-29T02:42:26Z","abstract_excerpt":"In this paper, we study the boundary value problem of the classical semilinear parabolic equations $$ u_t-\\Delta u=|u|^{p-1}u, \\ \\ in \\ \\ \\Omega\\times (0,T) $$ and $u=0$ on the boundary $\\partial\\Omega\\times [0,T)$ and $u=\\phi$ at $t=0$, where $\\Omega\\subset R^n$ is a compact $C^1$ domain, $1<p\\leq p_S$ is a fixed constant, and $\\phi\\in C^2_0(\\Omega)$ is a given smooth function. Introducing new idea, we show that there are two sets $\\tilde{W}$ and $\\tilde{Z}$ such that for $\\phi\\in W$, there is a global positive solution $u(t)\\in \\tilde{W}$ with $h^1$ omega limit $\\{0\\}$ and for $\\phi\\in \\tild"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5861","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"}