{"paper":{"title":"Convergence rates of the front tracking method for conservation laws in the Wasserstein distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Susanne Solem","submitted_at":"2018-04-23T09:52:56Z","abstract_excerpt":"We prove that front tracking approximations to entropy solutions of scalar conservation laws with convex fluxes converge at a rate of $\\Delta x^2$ in the 1-Wasserstein distance $W_1$. Assuming positive initial data, we also show that the approximations converge at a rate of $\\Delta x$ in the $\\infty$-Wasserstein distance $W_\\infty$. Moreover, from a simple interpolation inequality between $W_1$ and $W_\\infty$ we obtain convergence rates in all the $p$-Wasserstein distances: $\\Delta x^{1+1/p}$, $p \\in [1,\\infty]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08311","kind":"arxiv","version":4},"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"}