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| 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Ḣq s1-Ḣps0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). |
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| EXISTENCE OF SOLUTIONS TO THE INITIAL VALUE PROBLEM OF SEMI-LINEAR GENERALIZED TRICOMI EQUATION |
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ZHANG Kang-qun,LI Yu-chen
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| 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 Ḣq s1-Ḣps0 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 |
