{"paper":{"title":"A probabilistic algorithm approximating solutions of a singular PDE of porous media type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","stat.AP"],"primary_cat":"math.PR","authors_text":"ENSTA Paris Tech), Fran\\c{c}ois Cuvelier (LAGA), Francesco Russo (ENSTA Paris Tech, INRIA Rocquencourt), Nadia Belaribi (LAGA","submitted_at":"2010-11-13T06:24:02Z","abstract_excerpt":"The object of this paper is a one-dimensional generalized porous media equation (PDE) with possibly discontinuous coefficient $\\beta$, which is well-posed as an evolution problem in $L^1(\\mathbb{R})$. In some recent papers of Blanchard et alia and Barbu et alia, the solution was represented by the solution of a non-linear stochastic differential equation in law if the initial condition is a bounded integrable function. We first extend this result, at least when $\\beta$ is continuous and the initial condition is only integrable with some supplementary technical assumption. The main purpose of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3107","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"}