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Differential and Algebraic Riccati Equations with Application to Boundary/Point Control Problems: Continuous Theory and Approximation Theory [1991]
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1. Introduction: Two abstract classes; statement of main problems
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2. Abstract differential Riccati equation for the first class subject to the analyticity assumption (H.1)=(1.5)
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3. Abstract differential Riccati equations for the second class subject to the trace regularity assumption (H.2)=(1.6)
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4. Abstract differential Riccati equations for the second class subject to the regularity assumptions (H.2<Subscript>R</Subscript>)=(1.8)
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5. Abstract algebraic Riccati equations: Existence and uniqueness
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6. Examples of partial differential equation problems satisfying (H.1)
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7. Examples of partial differential equation problems satisfying (H.2)
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8. Example of a partial differential equation problem satisfying (H.2<Subscript>R</Subscript>)
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9. Numerical approximations of the solution to the abstract differential and algebraic Riccati equations
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10. Examples of numerical approximation for the classes (H.1) and (H.2)
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11. Conclusions