Cauchy problem for quasiparabolic factorized differential equations with variable domains of smoothed operators

We prove existence, uniqueness, and stability theorems for strong solutions of Cauchy problems for quasiparabolic factorized operator-differential equations with variable domains. For the first time, we derive a recursion formula for strong solutions of Cauchy problems, where recursion goes over the number of operator-differential factors in these equations. We prove the well-posed solvability (in the strong sense) for new mixed problems for partial differential equations with time-dependent coefficients in the boundary conditions.