Existence and uniqueness of the solution of initial boundary value problem for a class of equations with complex-valued coefficients is treated in this work. These equations behave like parabolic ones, though in time they may transform from parabolic to Schrodinger type or even to antiparabolic type. Note that for the equations of corresponding spectral problems the arguments of the roots of characteristic polynomials in the sense of Birkhoff are not constant.
Mamedov et al. (2025) studied this question.