In this paper we discuss the fundamental solution of the Keldysh type operator Lαu■2ux2+y2yuy2+αuy1,which is a basic mixed type operator different from the Tricomi operator.The fundamental solution of the Keldysh t...In this paper we discuss the fundamental solution of the Keldysh type operator Lαu■2ux2+y2yuy2+αuy1,which is a basic mixed type operator different from the Tricomi operator.The fundamental solution of the Keldysh type operator withα>-1/2 is obtained.It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator.Particularly,the fundamental solution of the Keldysh type operator withα<1/2 has to be defined by using the finite part of divergent integrals in the theory of distributions.展开更多
基金supported by the National Basic Research Program of China(Grant No.2006CB805902)National Natural Science Foundation of China(Grant No.10531020)the Research Foundation for Doctor Programme(Grant No.20050246001)
文摘In this paper we discuss the fundamental solution of the Keldysh type operator Lαu■2ux2+y2yuy2+αuy1,which is a basic mixed type operator different from the Tricomi operator.The fundamental solution of the Keldysh type operator withα>-1/2 is obtained.It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator.Particularly,the fundamental solution of the Keldysh type operator withα<1/2 has to be defined by using the finite part of divergent integrals in the theory of distributions.
