{"paper":{"title":"On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Espen R. Jakobsen, F\\'elix del Teso, J{\\o}rgen Endal","submitted_at":"2016-10-07T10:53:17Z","abstract_excerpt":"We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form $$\\partial_tu-A\\varphi(u)=0.$$ These equations are possibly degenerate nonlinear diffusion equations with a general nondecreasing continuous nonlinearity $\\varphi$ and the largest class of linear symmetric nonlocal diffusion operators $A$ considered so far. The operators are defined from a bilinear energy form $\\mathcal{E}$ and may be degenerate and have some $x$-dependence. The fractional Laplacian, symmetric finite differences, and any generator o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02221","kind":"arxiv","version":3},"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"}