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

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.
Published
25.11.2004
How to Cite
VlasenkoL. A., Piven’A. L., and RutkasA. G. “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.
Section
Research articles