Abstract Riccati equations in an L1 space of finite measure and applications to transport theory

Jonq Juang*, Paul Nelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider operator‐valued Riccati initial‐value problems of the form R′(t) + TR(t) + R(t)T = TA(t) + TB(t)R(t) + R(t)TC(t) + R(t)TD(t)R(t), R(0) = R0. Here A to D and R0 have values as non‐negative bounded linear operators in L1 (μ), where μ is a finite measure, and T is a closed non‐negative operator in L1 (μ) satisfying additional technical conditions. For such problems the notion of strongly mild solutions is defined, and local existence and uniqueness theorems for such solutions are established. The results of the analysis are applied to the reflection kernels with both isotropically scattering homogeneous and anisotropically scattering inhomogeneous medium.

Original languageEnglish
Pages (from-to)53-67
Number of pages15
JournalMathematical Methods in the Applied Sciences
Volume12
Issue number1
DOIs
StatePublished - 1 Jan 1990

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