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E-raamat: Distributed Systems with Persistent Memory: Control and Moment Problems

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Distributed Systems with Persistent Memory: Control and Moment ProblemsSuurem pilt
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The subject of the book includes the study of control problems for systems which are encountered in viscoelasticity, non-Fickian diffusion and thermodynamic with memory. The common feature of these systems is that memory of the whole past history persists in the future. This class of systems is actively studied now, as documented in the recent book. This book will attract a diversified audience, in particular, engineers working on distributed systems, and applied mathematicians. Background of mathematics are the elements of functional analysis, which is now standard among people working on distributed systems, and the author describes very clearly the instruments which are used at every step.

Arvustused

The book introduces all of the tools of functional analysis which are used in the proofs and each chapter contains more than ten problems . All these make reading interesting both for mathematicians and engineers working on distributed systems. (Sergei A. Ivanov, Mathematical Reviews, January, 2016)

1 An Example
1(26)
1.1 The Goal of This
Chapter and Preliminaries
1(3)
1.2 The System with Persistent Memory
4(6)
1.2.1 Finite Propagation Speed
6(2)
1.2.2 A Formula for the Solutions and a Control Problem
8(2)
1.3 Background of Functional Analysis
10(14)
1.3.1 Weak Topology in a Hilbert Spaces
11(1)
1.3.2 Operators and Resolvents
12(1)
1.3.3 Compact Operators
13(1)
1.3.4 Fixed Point and Equations
14(1)
1.3.5 Volterra Integral Equations
15(2)
1.3.6 Test Functions and Distributions
17(2)
1.3.7 Sobolev Spaces
19(2)
1.3.8 Sobolev Spaces and the Laplace Operator
21(3)
1.4 Problems to Chap. 1
24(3)
2 The Model and Preliminaries
27(30)
2.1 The Goal of This
Chapter and the System with Persistent Memory
27(8)
2.1.1 The Wave Equation
32(3)
2.2 The Solutions of the System with Memory
35(5)
2.3 Description of the Control Problems
40(2)
2.4 Useful Transformations
42(5)
2.4.1 Finite Propagation Speed
45(2)
2.5 Final Comments
47(1)
2.6 The Derivation of the Models
48(7)
2.6.1 Thermodynamics with Memory and Nonfickian Diffusion
48(2)
2.6.2 Viscoelasticity
50(2)
2.6.3 The Special Case of the Telegraphers' Equation
52(3)
2.7 Problems to Chap. 2
55(2)
3 Moment Problems and Exact Controllability
57(30)
3.1 The Goal of This
Chapter and the Moment Problem
57(4)
3.1.1 A Worked Example
58(3)
3.2 Properties of the Moment Operator When Y = l2
61(4)
3.3 Riesz Sequences and Moment Problems
65(5)
3.4 Perturbations of Riesz Sequences
70(13)
3.4.1 Riesz Sequences of Exponentials in L2 Spaces
75(2)
3.4.2 A Second Worked Example
77(6)
3.5 Problems to Chap. 3
83(4)
4 Controllability of the Wave Equation
87(12)
4.1 Introduction and the Goal of This
Chapter
87(2)
4.2 Hidden Regularity and Observation Inequality
89(3)
4.2.1 Consequences of Controllability on the Eigenvectors
90(2)
4.3 Controllability and Moment Problem
92(3)
4.4 Problems to Chap. 4
95(4)
5 Systems with Persistent Memory: Controllability via Moment Methods
99(24)
5.1 Introduction and the Goal of This
Chapter
99(2)
5.2 Moment Problem and Controllability of Viscoelastic Systems
101(3)
5.3 The Proof of Controllability
104(13)
5.3.1 Step A: the Functions Zn(t) and Rn(t)
104(2)
5.3.2 Step B: Closeness to a Riesz Sequence
106(5)
5.3.3 Step C: ω-Independence
111(6)
5.4 An Application: Source Identification
117(3)
5.5 Problems to Chap. 5
120(3)
6 Systems with Persistent Memory: The Observation Inequality
123(20)
6.1 Introduction and the Goal of This
Chapter
123(1)
6.2 Hidden Regularity for Systems with Persistent Memory, and a Test for the Solutions
124(7)
6.2.1 Controllability and the Observation Inequality
129(2)
6.3 The Observation Inequality for Systems with Memory
131(9)
6.3.1 Step A: Extension and Derivatives of the Solutions
133(2)
6.3.2 Step B: Propagation of Singularities
135(3)
6.3.3 Step C: End of the Proof
138(2)
6.4 Problems to Chap. 6
140(3)
References 143(6)
Series Editors' Biographies 149(2)
Index 151
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