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  • Open Access
  • © 2022

Evolutionary Equations

Picard's Theorem for Partial Differential Equations, and Applications

Birkhäuser
  • This book is open access, which means that you have free and unlimited access

  • Provides self-contained and comprehensive round up of the theory of evolutionary equations

  • The matter is confined to elementary Hilbert space theory and complex analysis

  • Easy access to challenging theory of time-dependent partial differential equations

Part of the book series: Operator Theory: Advances and Applications (OT, volume 287)

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 1-13Open Access
  3. Unbounded Operators

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 15-30Open Access
  4. The Time Derivative

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 31-49Open Access
  5. Ordinary Differential Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 51-66Open Access
  6. The Fourier–Laplace Transformation and Material Law Operators

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 67-83Open Access
  7. Solution Theory for Evolutionary Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 85-102Open Access
  8. Examples of Evolutionary Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 103-117Open Access
  9. Causality and a Theorem of Paley and Wiener

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 119-130Open Access
  10. Initial Value Problems and Extrapolation Spaces

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 131-148Open Access
  11. Differential Algebraic Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 149-165Open Access
  12. Exponential Stability of Evolutionary Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 167-188Open Access
  13. Boundary Value Problems and Boundary Value Spaces

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 189-204Open Access
  14. Continuous Dependence on the Coefficients I

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 205-220Open Access
  15. Continuous Dependence on the Coefficients II

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 221-241Open Access
  16. Maximal Regularity

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 243-258Open Access
  17. Non-Autonomous Evolutionary Equations

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 259-273Open Access
  18. Evolutionary Inclusions

    • Christian Seifert, Sascha Trostorff, Marcus Waurick
    Pages 275-297Open Access
  19. Back Matter

    Pages 299-317

About this book

This open access book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner. Moreover, the strength of this method is demonstrated by a large variety of examples, showing the applicability of the approach of evolutionary equations in various fields. Additionally, a quantitative theory for evolutionary equations is developed.

The text is self-contained, providing an excellent source for a first study on evolutionary equations and a decent guide to the available literature on this subject, thus bridging the gap to state-of-the-art mathematical research.

Keywords

  • Open Access
  • Evolutionary equations
  • Maxwell's equations
  • Initial Boundary Value Problems
  • Mathematical Physics
  • Hilbert space approach
  • Heat Equation
  • Wave Equation
  • Elasticity
  • Differential Algebraic Equations
  • Exponential Stability
  • Homogenisation
  • Evolutionary Inclusions
  • Time-dependent partial differential equations
  • Coupled Systems
  • Causality

Authors and Affiliations

  • Institut für Mathematik, Technische Universität Hamburg, Hamburg, Germany

    Christian Seifert

  • Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany

    Sascha Trostorff

  • Institut für Angewandte Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Marcus Waurick

About the authors

Christian Seifert studied Mathematics with minor in Physics at Technische Universität Dresden and received his Diploma in Mathematics in 2009. He then moved to Technische Universität Chemnitz as research associate and obtained his doctoral degree in Mathematics in 2012. Since 2012 he is senior scientist at Technische Universität Hamburg, where he gained his Habilitation in Mathematics in 2021. Christian Seifert has been deputy professor at various Universities: from 2015 and 2016 at Ludwig-Maximilians-Universität München, at Technische Universität Clausthal from 2019 to 2020, and at Christian-Albrechts-Universität zu Kiel in 2021.

Christian Seifert contributed to more than 30 peer-reviewed journal publications mainly on evolution equations and operator theory.

Sascha Trostorff studied mathematics with minor in computer sciences at the TU Dresden, Germany. He graduated in 2008. In 2011 he received his PhD providing a general solution concept for evolutionary inclusions, that is, a certain generalisation of nonlinear partial differential equations. In 2018 he completed his habilitation thesis also at the TU Dresden connecting semi-groups methods and evolutionary equations as well as developing the understanding of exponential stability for a large class of evolutionary equations. Since 2019 he works as a lecturer at the Christian-Albrechts-Universität in Kiel, Germany.

Sascha Trostorff is author of approximately 40 peer-reviewed research papers and co-authored one book. His main research area is functional analysis and its applications to partial differential equations.

Marcus Waurick graduated in Mathematics with minor in Physics at TU Dresden in 2009. During his first employment at the Faculty of Civil Engineering he finished his PhD in 2011 on homogenisation theory and accepted a position at the Institut for Analysis at TU Dresden later this year. 2015 he took up a research post at the University of Bath. 2016 he finished his habilitation thesis. In 2017 he became Chancellor’s Fellow at the University of Strathclyde. 2020 he accepted a position at TU Hamburg as research associate and in November he became deputy professor at TU Bergakademie Freiberg. Since April 2021 he is appointed University Professor at TU Bergakademie Freiberg having the chair for Partial Differential Equations.

Marcus Waurick contributed to more than 60 research articles and 2 books. He was guest lecturer at several universities and went on longer research visits around the world. He received the Research Excellence Award 2018 from the University of Strathclyde and was appointed Guest Professor 2020/2021 at TU Graz, Austria.

Bibliographic Information

  • Book Title: Evolutionary Equations

  • Book Subtitle: Picard's Theorem for Partial Differential Equations, and Applications

  • Authors: Christian Seifert, Sascha Trostorff, Marcus Waurick

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-030-89397-2

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 2022

  • License: CC BY

  • Hardcover ISBN: 978-3-030-89396-5

  • Softcover ISBN: 978-3-030-89399-6

  • eBook ISBN: 978-3-030-89397-2

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XII, 317

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Differential Equations

Buying options

Softcover Book USD 49.99
Price excludes VAT (USA)
Hardcover Book USD 59.99
Price excludes VAT (USA)