{"paper":{"title":"The Cauchy problem for the Finsler heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Goro Akagi, Kazuhiro Ishige, Ryuichi Sato","submitted_at":"2017-10-02T02:02:43Z","abstract_excerpt":"Let $H$ be a norm of ${\\bf R}^N$ and $H_0$ the dual norm of $H$. Denote by $\\Delta_H$ the Finsler-Laplace operator defined by $\\Delta_Hu:=\\mbox{div}\\,(H(\\nabla u)\\nabla_\\xi H(\\nabla u))$. In this paper we prove that the Finsler-Laplace operator $\\Delta_H$ acts as a linear operator to $H_0$-radially symmetric smooth functions. Furthermore, we obtain an optimal sufficient condition for the existence of the solution to the Cauchy problem for the Finsler heat equation $$ \\partial_t u=\\Delta_H u,\\qquad x\\in{\\bf R}^N,\\quad t>0, $$ where $N\\ge 1$ and $\\partial_t:=\\partial/\\partial t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00456","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"}