{"paper":{"title":"A Dynamical Approach to Viscosity Solutions of Hamilton-Jacobi Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jun Yan, Lin Wang","submitted_at":"2013-12-04T09:18:15Z","abstract_excerpt":"In this paper, we consider the following Hamilton-Jacobi equation with initial condition: \\begin{equation*} \\begin{cases} \\partial_tu(x,t)+H(x,t,u(x,t),\\partial_xu(x,t))=0, u(x,0)=\\phi(x). \\end{cases} \\end{equation*} Under some assumptions on the convexity of $H(x,t,u,p)$ w.r.t. $p$, we develop a dynamical approach to viscosity solutions and show that there exists an intrinsic connection between viscosity solutions and certain minimal characteristics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1072","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"}