{"paper":{"title":"Critical parameters for reaction-diffusion equations involving space-time fractional derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erkan Nane, Jebessa B. Milena, Mohammud Foondun, Sunday A. Asogwa","submitted_at":"2018-09-19T14:51:21Z","abstract_excerpt":"We will look at reaction-diffusion type equations of the following type, $$\\partial^\\beta_tV(t,x)=-(-\\Delta)^{\\alpha/2} V(t,x)+I^{1-\\beta}_t[V(t,x)^{1+\\eta}].$$ We first study the equation on the whole space by making sense of it via an integral equation. Roughly speaking, we will show that when $0<\\eta\\leq\\eta_c$, there is no global solution other than the trivial one while for $\\eta>\\eta_c$, non-trivial global solutions do exist. We also study the equation on a bounded domain with Dirichlet boundary condition and show that the presence of the time derivative induces a significant change in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07226","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"}