Краевые задачи для ультрапараболических и квазиультрапараболических уравнений с меняющимся направлением эволюции

We examine the solvability of the boundary-value problems for the differential equation
\begin{gather*} h(t)u_t+(-1)^mD^{2m+1}_au-\Delta u+c(x,t,a)u=f(x,t,a); \\ x\in\Omega\subset \mathbb{R}^n, \quad 0<t<T, \quad 0<a<A, \quad D^k_a=\frac{\partial^k}{\partial a^k}, \end{gather*}
where the sign of the function $h(t)$ arbitrarily alternates in the interval $[0,T]$. The existence and uniqueness theorems of regular (i.e., possessing all generalized derivatives in the Sobolev sense) solutions are proved.