{"paper":{"title":"Accelerating solutions in integro-differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jimmy Garnier (BIOSP)","submitted_at":"2010-09-30T10:16:32Z","abstract_excerpt":"In this paper, we study the spreading properties of the solutions of an integro-differential equation of the form $u_t=J\\ast u-u+f(u).$ We focus on equations with slowly decaying dispersal kernels $J(x)$ which correspond to models of population dynamics with long-distance dispersal events. We prove that for kernels $J$ which decrease to $0$ slower than any exponentially decaying function, the level sets of the solution $u$ propagate with an infinite asymptotic speed. Moreover, we obtain lower and upper bounds for the position of any level set of $u.$ These bounds allow us to estimate how the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6088","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"}