摘要
In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized 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.
In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized 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.
基金
Supported by National Natural Science Foundation of China (Grant No.11001122)
Scientific Research Fund of Nanjing Institute of Technology (Grant No.YKJ201113)
