{"paper":{"title":"Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"{\\L}ukasz P{\\l}ociniczak","submitted_at":"2018-12-19T16:21:27Z","abstract_excerpt":"In this short note we consider a nonlinear and spatially nonlocal PDE modelling moisture evolution in a porous medium. We then show that it naturally arises as a description of superdiffusive jump phenomenon occurring in the medium. We provide a deterministic derivation which allows us to naturally incorporate the nonlinear effects. This reasoning shows that in our setting the so-called nonlocal pressure form of the porous medium equation is preferred as a description of the evolution. In that case the governing nonlocal operator is the fractional gradient rather than the fractional Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08058","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"}