Global solutions for operator Riccati equations with unbounded coefficients: A non‐linear semigroup approach

Hendrik J. Kuiper

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let X be a Banach space of real‐valued functions on [0, 1] and let ℒ(X) be the space of bounded linear operators on X. We are interested in solutions R:(0, ∞) → ℒ(X) for the operator Riccati equation (Formula Presented.) where T is an unbounded multiplication operator in X and the Bi(t)'s are bounded linear integral operators on X. This equation arises in transport theory as the result of an invariant embedding of the Boltzmann equation. Solutions which are of physical interest are those that take on values in the space of bounded linear operators on L1(0, 1). Conditions on X, R(0), T, and the coefficients are found such that the theory of non‐linear semigroups may be used to prove global existence of strong solutions in ℒ(X) that also satisfy R(t) ϵ ℒ(L1(0,1)) for all t ≥ 0.

Original languageEnglish (US)
Pages (from-to)317-336
Number of pages20
JournalMathematical Methods in the Applied Sciences
Volume18
Issue number4
DOIs
StatePublished - 1995

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Unbounded Coefficients
Nonlinear Semigroups
Riccati equations
Riccati Equation
Operator Equation
Bounded Linear Operator
Global Solution
Mathematical operators
Transport Theory
Multiplication Operator
Boltzmann equation
Unbounded Operators
Banach spaces
Strong Solution
Boltzmann Equation
Integral Operator
Global Existence
Linear Operator
Banach space
Invariant

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Global solutions for operator Riccati equations with unbounded coefficients : A non‐linear semigroup approach. / Kuiper, Hendrik J.

In: Mathematical Methods in the Applied Sciences, Vol. 18, No. 4, 1995, p. 317-336.

Research output: Contribution to journalArticle

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