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半线性广义Tricomi方程初值问题的解的存在性
张康群,李宇尘

作者	单位
张康群	南京工程学院数理部, 江苏南京 211167
李宇尘	南京工程学院数理部, 江苏南京 211167

摘要:

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Ḣ_q ^s₁-Ḣ_p^s₀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.

关键词: 广义Tricomi方程半线性加权估计存在性

DOI：

分类号:O175.21

基金项目:Supported by NNSF of China(11326152); NSF of Jiangsu Province of China (BK20130736) and NSF of Nanjing Institute of Technology of China (YKJ201339).

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

ZHANG Kang-qun,LI Yu-chen

Abstract:

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 Ḣ_q ^s₁-Ḣ_p^s₀ 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.

Key words: generalized Tricomi equation semi-linear weighted estimate existence