{"paper":{"title":"Linear and Nonlinear Heat Equations on a p-Adic Ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Anatoly N. Kochubei","submitted_at":"2017-08-09T13:44:18Z","abstract_excerpt":"We study the Vladimirov fractional differentiation operator $D^\\alpha_N$, $\\alpha >0, N\\in \\mathbb Z$, on a $p$-adic ball $B_N=\\{ x\\in \\mathbb Q_p:\\ |x|_p\\le p^N\\}$. To its known interpretations via restriction from a similar operator on $\\mathbb Q_p$ and via a certain stochastic process on $B_N$, we add an interpretation as a pseudo-differential operator in terms of the Pontryagin duality on the additive group of $B_N$. We investigate the Green function of $D^\\alpha_N$ and a nonlinear equation on $B_N$, an analog the classical porous medium equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03261","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"}