### 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 = T^{ρ} A(t)T^{1−ρ} + T^{ρ} B(t)T^{1−ρ} R(t) + R(t)T^{ρ}C(t) T^{1−ρ} + R(t)T^{ρ}D(t)T^{1−ρ} R(t), R(0)=R_{0}, 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 L^{1} (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 language | English (US) |
---|---|

Pages (from-to) | 475-500 |

Number of pages | 26 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 16 |

Issue number | 7 |

DOIs | |

State | Published - 1993 |

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

## Fingerprint Dive into the research topics of 'Parameter‐dependent operator equations of the Riccati type with application to transport theory'. Together they form a unique fingerprint.

## Cite this

*Mathematical Methods in the Applied Sciences*,

*16*(7), 475-500. https://doi.org/10.1002/mma.1670160703