A note on initial value problem for the generalized Tricomi equation in a mixed-type domain

被引：0
作者：
Kang Qun Zhang
机构：
[1] Nanjing Institute of Technology,Department of Mathematics and Physics
来源：
Acta Mathematica Sinica, English Series | 2013年 / 29卷
关键词：
Generalized Tricomi equation; semilinear; initial value problem; mixed-type domain; 35M10; 35G10; 35L70;
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摘要：
In this paper, we study the well-posedness of initial value problem for n-dimensional generalized Tricomi equation in the mixed-type domain {(t, x): t ∈ [−1,+∞), x ∈ ℝn} with the initial data given on the line t = −1 in Hadamard’s sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.
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页码：1581 / 1596
页数：15
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