SINGULAR-DISTURBED SINGLE-SPEED TRANSPORT TASK OF KAC TYPE IN UNLIMITED REGION
In recent decades, methods connected with the use of integral transformations in the field of direct and inverse transport problems with a small parameter have become widespread in mathematics. In connection with this, in this paper we study a singularly perturbed problem of Kac transfer in an unbounded domain. The solution of the problem is sought in the weight space. The uniqueness of the solution of the degenerate problem is determined. And also the condition of solvability and uniqueness of the solution of the original singularly perturbed problem in a weighted space is proved, where - is the weight function. In this case, the residual function is uniquely determined. We consider and prove the closeness of the solutions of a singularly perturbed problem and a degenerate problem in the indicated space, when the a priori information on the initial data is given by.