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

Eisenmann, Monika LU orcid ; Emmrich, Etienne and Mehrmann, Volker (2019) In Evolution Equations and Control Theory 8(2). p.315-342
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.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Contribution to journal
publication status
published
subject
in
Evolution Equations and Control Theory
volume
8
issue
2
pages
315 - 342
external identifiers
  • scopus:85068473113
ISSN
2163-2480
DOI
10.3934/eect.2019017
language
English
LU publication?
no
id
47e08e44-c181-49cd-a0d8-b49bf306b5b0
date added to LUP
2024-10-07 14:56:46
date last changed
2025-04-04 14:51:18
@article{47e08e44-c181-49cd-a0d8-b49bf306b5b0,
  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.}},
  author       = {{Eisenmann, Monika and Emmrich, Etienne and Mehrmann, Volker}},
  issn         = {{2163-2480}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{315--342}},
  series       = {{Evolution Equations and Control Theory}},
  title        = {{Convergence of the backward Euler scheme for the operator-valued Riccati differential equation with semi-definite data}},
  url          = {{http://dx.doi.org/10.3934/eect.2019017}},
  doi          = {{10.3934/eect.2019017}},
  volume       = {{8}},
  year         = {{2019}},
}