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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1484–1500, November, 2004.
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Vlasenko, L.A., Piven’, A.L. & Rutkas, A.G. Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order. Ukr Math J 56, 1766–1781 (2004). https://doi.org/10.1007/s11253-005-0150-6
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DOI: https://doi.org/10.1007/s11253-005-0150-6