{"paper":{"title":"Propagation of Reactions in Inhomogeneous Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrej Zlatos","submitted_at":"2014-01-06T19:46:10Z","abstract_excerpt":"Consider reaction-diffusion equation $u_t=\\Delta u + f(x,u)$ with $x\\in\\mathbb{R}^d$ and general inhomogeneous ignition reaction $f\\ge 0$ vanishing at $u=0,1$. Typical solutions $0\\le u\\le 1$ transition from $0$ to $1$ as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on $f$ we show that in dimensions $d\\le 3$, the Hausdorff distance of the super-level sets $\\{u\\ge\\epsilon\\}$ and $\\{u\\ge 1-\\epsilon\\}$ remains uniformly bounded in time for each $\\epsilon\\in(0,1)$. Thus, $u$ remains uniformly in time close to the charact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1175","kind":"arxiv","version":3},"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"}