{"paper":{"title":"On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huicheng Yin (Nanjing University), Ingo Witt (University of G\\\"ottingen), Zhuoping Ruan (Nanjing University)","submitted_at":"2012-11-02T00:47:57Z","abstract_excerpt":"In this paper, we are concerned with the local existence and singularity structure of low regularity solutions to the semilinear generalized Tricomi equation $\\p_t^2u-t^m\\Delta u=f(t,x,u)$ with typical discontinuous initial data $(u(0,x), \\p_tu(0,x))=(0, \\vp(x))$; here $m\\in\\Bbb N$, $x=(x_1, ..., x_n)$, $n\\ge 2$, and $f(t,x,u)$ is $C^{\\infty}$ smooth in its arguments. When the initial data $\\vp(x)$ is a homogeneous function of degree zero or a piecewise smooth function singular along the hyperplane ${t=x_1=0}$, it is shown that the local solution $u(t,x)\\in L^{\\infty}([0,T]\\times\\Bbb R^n)$ exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0334","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"}