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

Authors

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

Abstract

In Banach spaces, we investigate the differential equation nj=0Aju(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.

Published

25.11.2004

Issue

Section

Research articles

How to Cite

Vlasenko, L. A., et al. “Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 11, Nov. 2004, pp. 1484-00, https://umj.imath.kiev.ua/index.php/umj/article/view/3860.