{"paper":{"title":"Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kazuhiro Ishige, Tatsuki Kawakami","submitted_at":"2012-02-06T02:34:10Z","abstract_excerpt":"Let $u$ be a solution of the Cauchy problem for the nonlinear parabolic equation $$ \\partial_t u=\\Delta u+F(x,t,u,\\nabla u) \\quad in \\quad{\\bf R}^N\\times(0,\\infty), \\quad u(x,0)=\\varphi(x)\\quad in \\quad{\\bf R}^N, $$ and assume that the solution $u$ behaves like the Gauss kernel as $t\\to\\infty$. In this paper, under suitable assumptions of the reaction term $F$ and the initial function $\\varphi$, we establish the method of obtaining higher order asymptotic expansions of the solution $u$ as $t\\to\\infty$. This paper is a generalization of our previous paper, and our arguments are applicable to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1037","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"}