Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order - Vlasenko, L. A.; Piven’, A. L.; Rutkas, A. G. (Ukrains’kyi Matematychnyi Zhurnal, 2004)
In Banach spaces, we investigate the differential equation \(\mathop \sum olimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations.