{"paper":{"title":"On some degenerate non-local parabolic equation associated with the fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ciprian G. Gal, Mahamadi Warma","submitted_at":"2015-09-10T12:50:11Z","abstract_excerpt":"We consider a degenerate parabolic equation associated with the fractional $% p $-Laplace operator $\\left( -\\Delta \\right) _{p}^{s}$\\ ($p\\geq 2$, $s\\in \\left( 0,1\\right) $) and a monotone perturbation growing like $\\left\\vert s\\right\\vert ^{q-2}s,$ $q>p$ and with bad sign at infinity as $\\left\\vert s\\right\\vert \\rightarrow \\infty $. We show the existence of locally-defined strong solutions to the problem with any initial condition $u_{0}\\in L^{r}(\\Omega )$ where $r\\geq 2$ satisfies $r>N(q-p)/sp$. Then, we prove that finite time blow-up is possible for these problems in the range of parameters "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03130","kind":"arxiv","version":2},"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"}