Parameter‐dependent operator equations of the Riccati type with application to transport theory

Hendrik J. Kuiper, Tapas Mazumdar

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We obtain an existence result for global solutions to initial‐value problems for Riccati equations of the form R′(t) + TR(t) + R(t)T = Tρ A(t)T1−ρ + Tρ B(t)T1−ρ R(t) + R(t)TρC(t) T1−ρ + R(t)TρD(t)T1−ρ R(t), R(0)=R0, where 0 ⩽ ρ ⩽ 1 and where the functions R and A through D take on values in the cone of non‐negative bounded linear operators on L1 (0, W; μ). T is an unbounded multiplication operator. This problem is of particular interest in case ρ = 1 since it arisess in the theories of particle transport and radiative transfer in a slab. However, in this case there are some serious difficulties associated with this equation, which lead us to define a solution for the case ρ = 1 as the limit of solutions for the cases 0 < ρ < 1.

Original languageEnglish (US)
Pages (from-to)475-500
Number of pages26
JournalMathematical Methods in the Applied Sciences
Volume16
Issue number7
DOIs
StatePublished - 1993

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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