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Systems with Persistent Memory

Controllability, Stability, Identification

  • Book
  • © 2021

Overview

Authors:
  1. Luciano Pandolfi

    1. Department of Mathematics “G.L. Lagrange”, Politecnico di Torino (retired), Torino, Italy

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  • Attracts a diversified audience including engineers and mathematicians
  • Study of control problems for systems which are encountered in viscoelasticity, non-Fickian diffusion and thermodynamic with memory
  • Includes chapters on stability and on identification problems for systems with persistent memory

Part of the book series: Interdisciplinary Applied Mathematics (IAM, volume 54)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Preliminary Considerations and Examples

    • Luciano Pandolfi
    Pages 1-36

  3. Operators and Semigroups for Systems with Boundary Inputs

    • Luciano Pandolfi
    Pages 37-102

  4. The Heat Equation with Memory and Its Controllability

    • Luciano Pandolfi
    Pages 103-161

  5. The Wave Equation with Memory and Its Controllability

    • Luciano Pandolfi
    Pages 163-222

  6. The Stability of the Wave Equation with Persistent Memory

    • Luciano Pandolfi
    Pages 223-282

  7. Dynamical Algorithms for Identification Problems

    • Luciano Pandolfi
    Pages 283-329

  8. Final Miscellaneous Problems

    • Luciano Pandolfi
    Pages 331-352

  9. Back Matter

    Pages 353-366
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Keywords

About this book

This text addresses systems with persistent memory that are common mathematical models used in the study of viscoelasticity and thermodynamics with memory. In particular, this class of systems is used to model non-Fickian diffusion in the presence of complex molecular structures. Hence, it has wide applications in biology.

The book focuses on the properties and controllability of the archetypal heat and wave equations with memory and introduces the dynamic approach to identification problems and the basic techniques used in the study of stability.

The book presents several approaches currently used to study systems with persistent memory: Volterra equation in Hilbert spaces, Laplace transform techniques and semigroup methods. The text is intended for a diverse audience in applied mathematics and engineering and it can be used in PhD courses. Readers are recommended to have a background in the elements of functional analysis. Topics of functional analysis which younger readers may need to familiarize with are presented in the book.



Reviews

“The book is well-written in general. Many fascinating outcomes may be found in each chapter. As a result, Luciano Pandolfi’s book Systems with Persistent Memory: Controllability, stability and Identification is accessible to a wide audience, beginning with postgraduate students. It also gives mathematicians and research engineers an excellent starting point. On the other hand, the book is a wonderful resource for researchers working in this field.” (Udhayakumar Ramalingam, zbMATH 1491.93001, 2022)

Authors and Affiliations

  • Department of Mathematics “G.L. Lagrange”, Politecnico di Torino (retired), Torino, Italy

    Luciano Pandolfi

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Bibliographic Information

  • Book Title: Systems with Persistent Memory

  • Book Subtitle: Controllability, Stability, Identification

  • Authors: Luciano Pandolfi

  • Series Title: Interdisciplinary Applied Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-80281-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-80280-6Published: 28 October 2021

  • Softcover ISBN: 978-3-030-80283-7Published: 29 October 2022

  • eBook ISBN: 978-3-030-80281-3Published: 27 October 2021

  • Series ISSN: 0939-6047

  • Series E-ISSN: 2196-9973

  • Edition Number: 1

  • Number of Pages: X, 356

  • Number of Illustrations: 3 b/w illustrations, 15 illustrations in colour

  • Topics: Systems Theory, Control, Complex Systems, Functional Analysis

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