{"paper":{"title":"Oscillatory travelling wave solutions for coagulation equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Barbara Niethammer, Juan J.J.L. Velazquez","submitted_at":"2017-02-08T14:23:09Z","abstract_excerpt":"We consider Smoluchowski's coagulation equation with kernels of homogeneity one of the form $K_{\\varepsilon }(\\xi,\\eta) =\\big( \\xi^{1-\\varepsilon }+\\eta^{1-\\varepsilon }\\big)\\big ( \\xi\\eta\\big) ^{\\frac{\\varepsilon }{2}}$. Heuristically, in suitable exponential variables, one can argue that in this case the long-time behaviour of solutions is similar to the inviscid Burgers equation and that for Riemann data solutions converge to a traveling wave for large times. Numerical simulations in \\cite{HNV16} indeed support this conjecture, but also reveal that the traveling waves are oscillatory and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02437","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"}