{"paper":{"title":"On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation","license":"","headline":"","cross_cats":["nlin.PS"],"primary_cat":"patt-sol","authors_text":"Casilla 306, Chile), M. C. Depassier (Facultad de F\\'isica, P. Universidad Cat\\'olica de Chile, R. D. Benguria, Santiago 22","submitted_at":"1994-03-08T18:38:00Z","abstract_excerpt":"We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently localized initial conditions evolve in time into a monotonic front which propagates with speed $c^*$ such that $2 \\sqrt{f'(0)} \\leq c^* < 2 \\sqrt{\\sup(f(u)/u)}$. The lower value $c_L = 2 \\sqrt{f'(0)}$ is that predicted by the linear marginal stability speed selection mechanism. We derive a new lower bound on the the speed of the selected front, this bound d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"patt-sol/9403001","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"}