2018
Том 70
№ 12

# Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order

Abstract

In Banach spaces, we investigate the differential equation $\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0$ 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.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 11, pp 1766-1781.

Citation Example: Piven’ A. L., Rutkas A. G., Vlasenko L. A. Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order // Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1484-1500.

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