{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GYBWFED6HRIEXUA4IKC5SIVVIL","short_pith_number":"pith:GYBWFED6","schema_version":"1.0","canonical_sha256":"360362907e3c504bd01c4285d922b542cd6261edceb6f60526844954eaaa042b","source":{"kind":"arxiv","id":"1810.12748","version":1},"attestation_state":"computed","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 $11$, 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