A Modern Framework Based on Time-Tested Material
A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering presents functional analysis as a tool for understanding and treating distributed parameter systems. Drawing on his extensive research and teaching from the past 20 years, the author explains how functional analysis can be the basis of modern partial differential equation (PDE) and delay differential equation (DDE) techniques.
Recent Examples of Functional Analysis in Biology, Electromagnetics, Materials, and Mechanics
Through numerous application examples, the book illustrates the role that functional analysis-a classical subject-continues to play in the rigorous formulation of modern applied areas. The text covers common examples, such as thermal diffusion, transport in tissue, and beam vibration, as well as less traditional ones, including HIV models, uncertainty in noncooperative games, structured population models, electromagnetics in materials, delay systems, and PDEs in control and inverse problems. For some applications, computational aspects are discussed since many problems necessitate a numerical approach.
Preface
Chapter 1 : Introduction to Functional Analysis in Applications
Chapter 2 : Semigroups and Infinitesimal Generators
Chapter 3 : Generators
Chapter 4 : Adjoint Operators and Dual Spaces
Chapter 5 : Gelfand Triple, Sesquilinear Forms, and Lax-Milgram
Chapter 6 : Analytic Semigroups
Chapter 7 : Abstract Cauchy Problems
Chapter 8 : General Second-Order Systems
Chapter 9 : Weak Formulations for Second-Order Systems
Chapter 10 : Inverse or Parameter Estimation Problems
Chapter 11 : "Weak" or "Variational Form"
Chapter 12 : Finite Element Approximations and the Trotter-Kato Theorems
Chapter 13 : Delay Systems : Linear and Nonlinear
Chapter 14 : Weak Convergence and the Prohorov Metric in Inverse Problems
Chapter 15 : The Prohorov Metric in Optimization and Optimal Design Problems
Chapter 16 : Control Theory for Distributed Parameter Systems
Chapter 17 : Families of Approximate Control Problems
References
Index
