Strong Solutions for Infinite-Dimensional Riccati Equations Arising in Transport Theory

The main result gives conditions under which the Riccati equation $S'(t) = A(t)S(t) + S(t)B(t) + S(t)C(t)S(t) + D(t)$ with initial condition $S(0) = S_0 $ has a strongly differentiable solution. In addition, equations of more general form, but with more restrictive initial conditions, are shown...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 11; no. 2; pp. 211 - 222
Main Authors Kuiper, Hendrik J., Shew, Steven M.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.03.1980
Subjects
Control theory
Hilbert space
Hypotheses
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Summary:The main result gives conditions under which the Riccati equation $S'(t) = A(t)S(t) + S(t)B(t) + S(t)C(t)S(t) + D(t)$ with initial condition $S(0) = S_0 $ has a strongly differentiable solution. In addition, equations of more general form, but with more restrictive initial conditions, are shown to have solutions which are differentiable with respect to the uniform topology. These results, as well as their proofs, are discussed in the context of an important problem in transport theory.
ISSN:0036-1410
1095-7154
DOI:10.1137/0511020