{"paper":{"title":"Global Existence and Large Time Asymptotic Bounds of $L^{infty}$ Solutions of Thermal Diffusive Combustion Systems on $R^{n}$","license":"","headline":"","cross_cats":["nlin.CD"],"primary_cat":"chao-dyn","authors_text":"AZ), Ecole polytechnique, France.), J. Xin (Department of Mathematics University of Arizona Tucson, Palaiseau, P. Collet (Centre de Physique Th'eorique Laboratoire CNRS","submitted_at":"1994-12-05T10:59:26Z","abstract_excerpt":"We consider the initial value problem for the thermal-diffusive combustion systems of the form:\n  $u_{1,t}= Delta_{x}u_1 - u_1 u_2^m$, $u_{2,t}= d Delta_{x} u_2 + u_1 u_2^m$,\n  $x in R^{n}$, $n geq 1$, $m geq 1$, $d > 1$,\n with bounded uniformly continuous nonnegative initial data. For such initial data, solutions can be simple traveling fronts or complicated domain walls. Due to the well-known thermal-diffusive instabilities when $d$, the Lewis number, is sufficiently away from one, front solutions are potentially chaotic. It is known in the literature that solutions are uniformly bounded in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9412003","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"}