{"paper":{"title":"Asymptotic expansions of solutions of fractional diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hironori Michihisa, Kazuhiro Ishige, Tatsuki Kawakami","submitted_at":"2016-10-31T05:35:49Z","abstract_excerpt":"In this paper we obtain the precise description of the asymptotic behavior of the solution $u$ of $$ \\partial_t u+(-\\Delta)^{\\frac{\\theta}{2}}u=0\\quad\\mbox{in}\\quad{\\bf R}^N\\times(0,\\infty), \\qquad u(x,0)=\\varphi(x)\\quad\\mbox{in}\\quad{\\bf R}^N, $$ where $0<\\theta<2$ and $\\varphi\\in L_K:=L^1({\\bf R}^N,\\,(1+|x|)^K\\,dx)$ with $K\\ge 0$. Furthermore, we develop the arguments in [15] and [18] and establish a method to obtain the asymptotic expansions of the solutions to a nonlinear fractional diffusion equation $$ \\partial_t u+(-\\Delta)^{\\frac{\\theta}{2}}u=|u|^{p-1}u\\quad\\mbox{in}\\quad{\\bf R}^N\\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09789","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"}