Keldysh型方程在矩形区域上的解的适定性

Well-posedness of Solution of Keldysh Type Equation in the Rectangular Domain

研究Keldysh型方程在区域Ω={(t_(1),t_(0))×(0,π):t_(1)≤0,t 0>0}上的Dirichlet问题的适定性.当t_(1)=0时,建立退化双曲型方程的解,并得到一个先验加权估计;当t_(1)<0时,在Hadamard's意义下构造混合型方程的一个不连续依赖给定边值的特解.以此说明其Dirichlet问题解的不适定性.

In this paper we study Dirichlet problem of an elliptic-hyperbolic Keldysh type equation in the domain{Ω={(t_(1),t_(2))}×(0,π):t_(1)≤0,t 0>0}.For t_(1)=0,we establish the solution of degenerate hyperbolic equation and derive its priori weighted estimate.For t_(1)<0,we show the ill-posedness of Dirichlet problem of mixed type equation in Hadamard’s sense by constructing a counterexample.