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Control theory for partial differential equations : continuous and approximation theories. 1, Abstract parabolic systems /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2000.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 74. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- ""Cover""; ""Series Page""; ""Dedication""; ""Title""; ""Copyright""; ""Contents""; ""Preface""; ""Acknowledgments for the First Two Volumes""; ""0 Background""; ""0.1 Some Function Spaces Used in Chapter 1""; ""0.2 Regularity of the Variation of Parameter Formula When eAt Is a s.c. Analytic Semigroup""; ""0.2.1 Comments on the Space [X, Y]�""; ""0.2.2 Cases Where [D(A),Y]� =D((�A)�)""; ""0.2.3 Comments on the Proof of Proposition 0.1""; ""Properties (0.9), (0.14)""; ""Property (0.10)""; ""Properties (0.11), (0.12)""; ""Properties (0.13)""; ""0.3 The Extrapolation Space [D(A*)]'""
- ""0.4 Abstract Setting for Volume I. The Operator LT in (1.1.9), or LsT in (1.4.1.6), of Chapter 1""""References and Bibliography""; ""1 Optimal Quadratic Cost Problem Over a Preassigned Finite Time Interval: Differential Riccati Equation""; ""1.1 Mathematical Setting and Formulation of the Problem""; ""1.2 Statement of Main Results""; ""1.2.1 The Nonsmoothing Case. Theorem 1.2.1.1: Existence of a Riccati Operator""; ""1.2.2 Two Smoothing Cases. Theorem 1.2.2.1: Classical Differential Riccati Equation and Uniqueness of the Riccati Operator. Theorem 1.2.2.2""; ""1.3 Orientation""
- ""1.4 Proof of Theorem 1.2.1.1 with GLr Closed""""1.4.1 Optimality. Explicit Representation Formulas for the Optimal Pair {u0, y0}""; ""1.4.2 L2-Estimatesfor {u0,y0} and Zf-Estimate for Gy0(T; . ; x). Limit Relations as s â?? T""; ""1.4.3 Definition of Operators Î? (T, s ) and P(t) and First Properties""; ""1.4.4 Smoothing Properties of Ls and Ls* at t = T, and on Lp(s,T; . )-Spaces. Pointwise Estimates for u0(t, s; x), y0(t, s; x), and P(t)""; ""1.4.5 Smoothing Properties of Ls and Ls* at t = s. Pointwise Regularity of du0(t,s; x)/dt and dy0(t,s; x)/dt for s < t < T, x ε Y""
- ""1.7 The Theory of Theorem 1.2.1.1 Is Sharp. Counterexamples When GLÏ? Is Not Closable""""1.7.1 Counterexample to the Existence of the Optimal Control u0 When GLÏ? Is Not Closable""; ""1.7.2 Assumption (1.2.1.26) Is Only Sufficientfor GLÏ? to Be Closed""; ""1.8 Extension to Unbounded Operators R and G""; ""1.8.1 The Case Where R E £(1)( (â€?A)Î?); Z) and G E £(D((â€?A)Î?); Zf), 0""; ""1A Proof of Lemma 1.5.1.l(iii)""; ""Notes on Chapter 1""