{"paper":{"title":"Global existence for a Leibenson type equation with reaction on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francescantonio Oliva, Francesco Petitta, Giulia Meglioli","submitted_at":"2025-05-13T07:27:25Z","abstract_excerpt":"We show a global existence result for a doubly nonlinear porous medium type equation of the form $$u_t = \\Delta_p u^m +\\, u^q$$ on a complete and non-compact Riemannian manifold $M$ of infinite volume. Here, for $1<p<N$, we assume $m(p-1)\\ge1$, $m>1$ and $q>m(p-1)$. In particular, under the assumptions that $M$ supports the Sobolev inequality, we prove that a solution for such a problem exists globally in time provided $q>m(p-1)+\\frac pN$ and the initial datum is small enough; namely, we establish an explicit bound on the $L^\\infty$ norm of the solution at all positive times, in terms of the $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08304","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.08304/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}