Ukrainian Mathematical Journal

, Volume 56, Issue 11, pp 1766–1781 | Cite as

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

  • L. A. Vlasenko
  • A. L. Piven’
  • A. G. Rutkas
Article

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 Aj (generally speaking, the operator coefficient An 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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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • L. A. Vlasenko
    • 1
  • A. L. Piven’
    • 1
  • A. G. Rutkas
    • 1
  1. 1.Kharkov National UniversityKharkovUkraine

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