Abstract:
We consider a particular case of the earlier studied by the author second order degenerate differential operator with the same assumptions and designations. We focus on the study of the effects associated with the “strong” degeneration. The problem is solved to be used in further researches of formally conjugated (coupled transposition operation) equation and also for obtaining some theorems of existence and uniqueness for generalized solutions of formally conjugated equations from the proved theorem. The use of the following results is reduced to the operator equations in the simplest case. We study existence and uniqueness of the generalized solution of the first boundary value problem for the given equation using the operator theory and obtain the generalized solution to the equation in the case connected with “strong” degeneration. The results will be used in the future for research of equations with model operators which arise in mathematical modeling of various physical processes.
Keywords:Hilbert space, degenerate differential operator, generalized solution, “weak” degeneration, “strong"” degeneration, nonhomogeneous equation, general solution, partial solution, model operator.
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