2021-12-01T01:09:50Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000400482021-03-02T02:38:29ZGevrey Regularity in Time of Solutions to Nonlinear Partial Differential EquationsTahara, Hidetoshi92499415Gevrey classGevrey regularitytime regularitysolutionnonlinear PDEThe paper considers nonlinear partial differential equations tγ(∂/∂t)mu = G(t, x, {(∂/∂t)j(∂/∂x)αu}j<m,|α|≦L) (with γ ≧ 0 and 1 ≦ m ≦ L) in Gevrey classes, and gives a sufficient condition for the following assertion to be valid: if a solution u(t, x) is in C∞ class with respect to the time variable t and in the Gevrey class E{σ} in the space variable x, then it is in the Gevrey class E{s} also with respect to the time variable for a suitable s. The index s of the time regularity is precisely estimated by the data of the equation. In a particular case, the necessity of the condition is also discussed.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2011-09-20application/pdfJournal of mathematical sciences, the University of Tokyo11867137AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40048/files/jms180104.pdfeng