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Our research focuses on examining a mixed problem associated with a second-order parabolic equation that features temporal mixing and variable coefficients, subject to non-local and non-self-adjoint boundary conditions. We establish the problem’s unique solvability by imposing specific conditions on the provided data, utilizing a combination of residue and contour integral methods. Additionally, our study produces an explicit analytical solution for addressing the problem at hand.
Ahmadov et al. (Mon,) studied this question.