半线性广义Tricomi方程初值问题的解的存在性

摘要

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)sq1 - (H)sp0 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 infinity in the weighted estimates.%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)sq1-(H)sp0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.