{"paper":{"title":"Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eunkyung Ko, Michaela Zahradn\\'ikov\\'a, Pavel Dr\\'abek, Soyeun Jung","submitted_at":"2026-05-30T09:26:33Z","abstract_excerpt":"We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \\geq H^*:=\\sup_{0<u \\leq \\theta} \\big(-\\frac{1}{u} \\int_0^u h(\\sigma)\\,d\\sigma \\big)$, where $c$ denotes the wave speed, $\\theta\\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \\cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \\geq -\\min_{u\\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\\ge H^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}