{"paper":{"title":"A general fractional porous medium equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Rodr\\'iguez, Arturo de Pablo, Fernando Quir\\'os, Juan Luis V\\'azquez","submitted_at":"2011-04-02T09:16:17Z","abstract_excerpt":"We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \\{ll} \\dfrac{\\partial u}{\\partial t} + (-\\Delta)^{\\sigma/2} (|u|^{m-1}u)=0, & \\qquad x\\in\\mathbb{R}^N,\\; t>0,  [8pt] u(x,0) = f(x), & \\qquad x\\in\\mathbb{R}^N.%. $$ We consider data $f\\in L^1(\\mathbb{R}^N)$ and all exponents $0<\\sigma<2$ and $m>0$. Existence and uniqueness of a weak solution is established for $m> m_*=(N-\\sigma)_+ /N$, giving rise to an $L^1$-contraction semigroup. In addition, we obtain the main qualitative properties of these solutions. In the lower range $0<"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0306","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"}