半线性广义Tricomi方程初值问题的解的存在性（英文）

EXISTENCE OF SOLUTIONS TO THE INITIAL VALUE PROBLEM OF SEMI-LINEAR GENERALIZED TRICOMI EQUATION

本文研究了半线性广义Tricomi方程初值问题解的存在性.基于对两个傅立叶积分算子的H_q^(s_1)-H_p^(s_0)加权估计不等式,建立了半线性广义Tricomi方程在双曲半平面解的局部和全局存在性.同时,给出了解在退化区域附近的正则性损失和在无穷远处衰减律.

In this paper,we study the existence of solutions to the initial value problem of semi-linear generalized Tricomi equation with characteristic families coincided on t=0.Based on the inequality of_H s1q-_Hs0p estimates of two Fourier integral operators,we establish the local and global existence of solution for the semi-linear equation in hyperbolic half space.Meanwhile,we give the loss of regularities on degenerate domain and the decay rates when time tends to inˉnity in the weighted estimates.