{"paper":{"title":"Sup-norm estimates for parabolic systems with dynamic boundary conditions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Ciprian G. Gal","submitted_at":"2012-10-29T14:09:14Z","abstract_excerpt":"We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for certain reaction-diffusion systems that occur in mathematical biology and ecology. We devise several strategies which imply (uniform)}$L^{p} and}$L^{\\infty}$ estimates on the solutions for the initial value problems considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7671","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"}