{"paper":{"title":"Fujita blow up phenomena and hair trigger effect: the role of dispersal tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matthieu Alfaro (IMAG)","submitted_at":"2016-05-03T13:11:02Z","abstract_excerpt":"We consider the nonlocal diffusion equation $\\partial \\_t u=J*u-u+u^{1+p}$ in the whole of $\\R ^N$. We prove that the Fujita exponent  dramatically depends on the behavior of the Fourier transform of the kernel $J$ near the origin, which is linked to the tails of $J$. In particular, for compactly supported  or exponentially bounded  kernels, the Fujita exponent is the same as that of the nonlinear Heat equation $\\partial \\_tu=\\Delta u+u^{1+p}$. On the other hand, for kernels with algebraic tails, the Fujita exponent  is either of  the Heat type or of some related Fractional type, depending on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00891","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"}