{"paper":{"title":"The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jonathan D. Evans, Pablo Alvarez-Caudevilla, Victor A. Galaktionov","submitted_at":"2014-07-21T16:33:04Z","abstract_excerpt":"Fundamental global similarity solutions of the standard form u_\\g(x,t)=t^{-\\a_\\g} f_\\g(y), with the rescaled variable y= x/{t^{\\b_\\g}}, \\b_\\g= \\frac {1-n \\a_\\g}{10}, where \\a_\\g>0 are real nonlinear eigenvalues (\\g is a multiindex in R^N) of the tenth-order thin film equation (TFE-10) u_{t} = \\nabla \\cdot(|u|^{n} \\n \\D^4 u) in R^N \\times R_+, n>0, are studied. The present paper continues the study began by the authors in the previous paper\n  P. Alvarez-Caudevilla, J.D.Evans, and V.A. Galaktionov, The Cauchy problem for a tenth-order thin film equation I. Bifurcation of self-similar oscillatory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5554","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"}