{"paper":{"title":"Viscosity solutions for systems of parabolic variational inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Adrian Z\\u{a}linescu, Aurel R\\u{a}\\c{s}canu, Etienne Pardoux, Lucian Maticiuc","submitted_at":"2008-07-28T11:39:11Z","abstract_excerpt":"In this paper, we first define the notion of viscosity solution for the following system of partial differential equations involving a subdifferential operator:\\[\\{[c]{l}\\dfrac{\\partial u}{\\partial t}(t,x)+\\mathcal{L}_tu(t,x)+f(t,x,u(t,x))\\in\\partial\\phi (u(t,x)),\\quad t\\in[0,T),x\\in\\mathbb{R}^d, u(T,x)=h(x),\\quad x\\in\\mathbb{R}^d,\\] where $\\partial\\phi$ is the subdifferential operator of the proper convex lower semicontinuous function $\\phi:\\mathbb{R}^k\\to (-\\infty,+\\infty]$ and $\\mathcal{L}_t$ is a second differential operator given by $\\mathcal{L}_tv_i(x)={1/2}\\operatorname {Tr}[\\sigma(t,x)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4415","kind":"arxiv","version":2},"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"}