{"paper":{"title":"On convergence of solutions of fractal Burgers equation toward rarefaction waves","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Grzegorz Karch, Xiaojing Xu","submitted_at":"2007-02-05T00:14:10Z","abstract_excerpt":"In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\\partial^2_x)^{\\alpha/2} u+uu_x=0$ with $\\alpha\\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\\pm$ ($u_-<u_+$) as $x\\to \\pm\\infty$, respectively, then the corresponding solution converges toward the rarefaction wave, {\\it i.e.} the unique entropy solution of the Riemann problem for the nonviscous Burgers equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0702088/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}