Title:
A functional analysis framework for modeling, estimation and control in science and engineering
Author:
Banks, H. Thomas.
ISBN:
9781439880845
Publication Information:
Boca Raton, Fla. : CRC Press, 2012.
Physical Description:
xi, 268 p. : ill.
Contents:
1. Introduction to functional analysis in applications -- 2. Semigroups and infinitesimal generators -- 3. Generators -- 4. Adjoint operators and dual spaces -- 5. Gelfand triple, sesquilinear forms, and Lax-Milgram -- 6. Analytic semigroups -- 7. Abstract cauchy problems -- 8. General second-order systems -- 9. Weak formulations for second-order systems -- 10. Inverse or parameter estimation problems -- 11. 'Weak' or 'variational form' -- 12. Finite element approximations and the Trotter-Kato theorems -- 13. Delay systems : linear and nonlinear -- 14. Weak convergence and the Prohorov metric in inverse problems -- 15. The Prohorov metric in optimization and optimal design problems -- 16. Control theory for distributed parameter systems -- 17. Families of approximate control problems.
Abstract:
"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.
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