{"paper":{"title":"Viscous singular shock profiles for the Keyfitz-Kranzer system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ting-Hao Hsu","submitted_at":"2015-12-03T06:54:48Z","abstract_excerpt":"It was shown by Schecter (2004, J. Differential Equations, 205, 185-210), using the methods of Geometric Singular Perturbation Theory, that the Dafermos regularization $u_t+f(u)_x= \\epsilon tu_{xx}$ for the Keyfitz-Kranzer system admits an unbounded family of solutions. Inspired by that work, in this paper we provide a more intuitive approach which leads to a stronger result. In addition to the existence of viscous profiles, we also prove the weak convergence and show that the maximum of the solution is of order $\\epsilon^{-2}$. This asymptotic behavior is distinct from that obtained in the au"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00966","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"}