{"paper":{"title":"Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonio Segatti, Juan Luis Vazquez, Matteo Bonforte","submitted_at":"2015-05-12T21:06:56Z","abstract_excerpt":"We show non-existence of solutions of the Cauchy problem in $\\mathbb{R}^N$ for the nonlinear parabolic equation involving fractional diffusion $\\partial_t u + (-\\Delta)^s \\phi(u)= 0,$ with $0<s<1$ and very singular nonlinearities $\\phi$ . More precisely, we prove that when $\\phi(u)=-1/u^n$ with $n>0$, or $\\phi(u) = \\log u$, and we take nonnegative $L^1$ initial data, there is no (nonnegative) solution of the problem in any dimension $N\\ge 2$. We find the range of non-existence when $N=1$ in terms of $s$ and $n$. The range of exponents that we find for non-existence both for parabolic and ellip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03167","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"}