{"paper":{"title":"Analysis of a class of degenerate parabolic equations with saturation mechanisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juan Calvo","submitted_at":"2013-12-14T12:07:22Z","abstract_excerpt":"We analyze a family of degenerate parabolic equations with linear growth Lagrangian having the form $u_t=\\div (\\varphi(u)\\psi(\\nabla u/u))$. Here $|\\psi|\\le 1$ and saturates at infinity. We present a simple and natural set of assumptions on the functions $\\psi,\\varphi$, under which: 1) these equations fall in the framework provided by \\cite{ACMEllipticFLDE, ACMMRelat} and hence they are well posed, 2) we can ensure finite propagation speed for these models, 3) a Rankine--Hugoniot analysis on traveling fronts is also performed. On the particular case of $\\varphi(u)=u$ we get more detailed infor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4034","kind":"arxiv","version":5},"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"}