Sufficient conditions for regular solvability of an arbitrary order operator-differential equation with initial-boundary conditions

摘要: On this paper, for an arbitrary order operator-differential equation with the weight $e^{\frac{-\alpha t}{2}}, \alpha \in (-\infty ,+ \infty )$, in space $W^{n+m}_{2}(R_{+};H)$, we attain sufficient conditions well-posedness of a regular solvable boundary value problem. These are provided only by operator coefficients investigated where leading part has multiple characteristics. We prove connection between lower bound spectrum higher-order differential main and exponential also obtain estimations norms intermediate derivatives. apply results paper to mixed problem partial equations (HOPDs).