{"paper":{"title":"Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claude-Michel Brauner, Luca Lorenzi, Mingmin Zhang","submitted_at":"2019-01-04T14:24:55Z","abstract_excerpt":"In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermo-diffusive combustion, in the case of high Lewis numbers (${\\rm Le} >1$). The system of two parabolic PDEs is characterized by a free interface at which ignition temperature $\\Theta_i$ is reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a bifurcation parameter $m=\\Theta_i/(1-\\Theta_i)$ and a perturbation parameter $\\varepsilon= 1/{\\rm Le}$. The main result is the existence of a critical value $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01123","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"}