__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. 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. Front Cover......Page 1 Preface......Page 10 Acknowledgments......Page 12 Contents......Page 6 1. Introduction to Functional Analysis in Applications......Page 14 2. Semigroups and Infinitesimal Generators......Page 34 3. Generators......Page 38 4. Adjoint Operators and Dual Spaces......Page 60 5. Gelfand Triple, Sesquilinear Forms, and Lax-Milgram......Page 76 6. Analytic Semigroups......Page 94 7. Abstract Cauchy Problems......Page 108 8. General Second-Order Systems......Page 116 9. Weak Formulations for Second-Order Systems......Page 122 10. Inverse or Parameter Estimation Problems......Page 136 11. "Weak" or "Variational Form"......Page 150 12. Finite Element Approximations and the Trotter-Kato Theorems......Page 156 13. Delay Systems: Linear and Nonlinear......Page 164 14. Weak* Convergence and the Prohorov Metric in Inverse Problems......Page 190 15. The Prohorov Metric in Optimization and Optimal Design Problems......Page 210 16. Control Theory for Distributed Parameter Systems......Page 232 17. Families of Approximate Control Problems......Page 242 References......Page 254 "The result of lecture notes from courses the author has taught in applied functional analysis beginning in the late 1980s through the present, the choices of topics covered here are not purported to be comprehensive and even border on the eclectic. In contrast to classical PDE techniques, functional analysis is presented as a basis of modern partial and delay differential equation techniques. It is also somewhat different from the emphasis in usual functional analysis courses where functional analysis is a subdiscipline in its own right. Here it is treated as a tool to be used in understanding and treating distributed parameter systems"-- Provided by publisher
