Inverse Problem for Mixed-type Equation with an Elliptic Operator of Arbitrary Order

In this paper, we consider the inverse problem of determining the source function for a mixed-type equation with a positive elliptic operator. The existence and uniqueness of the solution of the posed inverse problem are proved. And also a generalized solution of the problem is introduced and the stability of such a solution is proved. At the end of the paper, a mixed-type equation with a non-negative elliptic operator is considered. It is proved that the corresponding inverse problem also has a unique solution, although, as is known, the forward problem for such an equation has more than one solution.

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