{"paper":{"title":"On semilinear Tricomi equations in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyin He, Huicheng Yin, Ingo Witt","submitted_at":"2018-10-27T07:49:07Z","abstract_excerpt":"For 1-D semilinear Tricomi equation $\\partial_t^2 u-t\\partial_x^2u=|u|^p$ with initial data $(u(0,x), \\partial_t u(0,x))$ $=(u_0(x), u_1(x))$, where $t\\ge 0$, $x\\in\\mathbb{R}$, $p>1$, and $u_i\\in C_0^\\infty(\\mathbb{R})$ ($i=0,1$), we shall prove that there exists a critical exponent $p_{\\rm crit}=5$ such that the small data weak solution $u$ exists globally when $p>p_{\\rm crit}$; on the other hand, the weak solution $u$, in general, blows up in finite time when $1<p<p_{\\rm crit}$. We specially point out that for 1-D semilinear wave equation $\\partial_t^2 v-\\partial_x^2v=|v|^p$, the weak soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12748","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"}