{"paper":{"title":"Action functional and quasi-potential for the Burgers equation in a bounded interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Alberto De Sole, Claudio Landim, Davide Gabrielli, Giovanni Jona-Lasinio, Lorenzo Bertini","submitted_at":"2010-04-13T16:32:24Z","abstract_excerpt":"Consider the viscous Burgers equation $u_t + f(u)_x = \\epsilon\\, u_{xx}$ on the interval $[0,1]$ with the inhomogeneous Dirichlet boundary conditions $u(t,0) = \\rho_0$, $u(t,1) = \\rho_1$.  The flux $f$ is the function $f(u)= u(1-u)$, $\\epsilon>0$ is the viscosity, and the boundary data satisfy $0<\\rho_0<\\rho_1<1$.  We examine the quasi-potential corresponding to an action functional, arising from non-equilibrium statistical mechanical models, associated to the above equation.  We provide a static variational formula for the quasi-potential and characterize the optimal paths for the dynamical p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2225","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"}