Conditional stability and regularizations of an initial-boundary value problem for a system of parabolic type equations with two degeneration lines

In this work, an ill-posed initial-boundary value problem for a system of parabolic type equations with two degeneration lines is considered, the eigenvalues of the problem and their corresponding eigenfunctions are found, an a priori estimate for the solution of the problem is obtained, in addition, theorems about the uniqueness and conditional stability of the solution of the problem are proved in the set of correctness and an approximate solution is constructed in the appropriate functional space.

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