{"paper":{"title":"Stochastic homogenization of a porous-medium type equation","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Stefania Patrizi","submitted_at":"2022-09-13T23:10:26Z","abstract_excerpt":"We consider the homogenization problem for the stochastic porous-medium type equation $\\p_{t} u^\\epsilon =\\Delta f\\left(T\\left(\\frac{x}{\\ep}\\right)\\om,u^\\ep\\right)$, with a well-prepared initial datum, where $f(T(y)\\om,u)$ is a stationary process, increasing in $u$, on a given probability space $(\\Om, \\mathcal{F}, \\mu)$ endowed with an ergodic dynamical system $\\{T(y)\\,:\\,y\\in\\R^N\\}$. Differently from the previous literature \\cite{afs,fs}, here we do not assume $\\Om$ compact. We first show that the weak solution $u^\\ep$ satisfies a kinetic formulation of the equation, then we exploit the theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.06342","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/2209.06342/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"}