{"paper":{"title":"Initial trace of positive solutions to fractional diffusion equation with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen, Laurent Veron (LMPT)","submitted_at":"2017-12-14T13:52:08Z","abstract_excerpt":"In this paper, we prove the existence of an initial trace T u of any positive solution u of the semilinear fractional diffusion equation (H) $\\partial$ t u + (--$\\Delta$) $\\alpha$ u + f (t, x, u) = 0 in R * + $\\times$ R N , where N $\\ge$ 1 where the operator (--$\\Delta$) $\\alpha$ with $\\alpha$ $\\in$ (0, 1) is the fractional Laplacian and f : R + $\\times$ R N  $\\times$ R + $\\rightarrow$ R is a Caratheodory function satisfying f (t, x, u)u $\\ge$ 0 for all (t, x, u) $\\in$ R + $\\times$ R N $\\times$  R +. We define the regular set of the trace T u as an open subset of R u $\\subset$ R N carrying a n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05223","kind":"arxiv","version":4},"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"}