English

Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data

Analysis of PDEs 2018-08-06 v2

Abstract

For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is generalized and used to obtain the existence of a solution to the approximation of the problem via a backward Euler scheme. Weak and strong convergence of the sequence of approximate solutions is established permitting a large class of right-hand sides and initial data.

Keywords

Cite

@article{arxiv.1803.11152,
  title  = {Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data},
  author = {Monika Eisenmann and Etienne Emmrich and Volker Mehrmann},
  journal= {arXiv preprint arXiv:1803.11152},
  year   = {2018}
}