Evolutionary Equations and Picard’s Theorem by Christian Seifert
Evolutionary Equations and Picard’s Theorem - Table of Contents
1. Introduction
2. Unbounded Operators
3. The Time Derivative
4. Ordinary Differential Equations
5. The Fourier–Laplace Transformation and Material Law Operators
6. Solution Theory for Evolutionary Equations
7. Examples of Evolutionary Equations
8. Causality and a Theorem of Paley and Wiener
9. Initial Value Problems and Extrapolation Spaces
10. Differential Algebraic Equations
11. Exponential Stability of Evolutionary Equations
12. Boundary Value Problems and Boundary Value Spaces
13. Continuous Dependence on the Coefficients I
14. Continuous Dependence on the Coefficients II
15. Maximal Regularity
16. Non-Autonomous Evolutionary Equations
17. Evolutionary Inclusions
A. Derivations of Main Equations
What You Will Learn in Evolutionary Equations and Picard’s Theorem
"Evolutionary Equations: Picard's Theorem for Partial Differential Equations, and Applications" by Christian Seifert, Sascha Trostorff, and Marcus Waurick is a rigorous mathematical text that explores a modern framework for solving partial differential equations (PDEs) using evolutionary methods. The book builds on Picard’s theorem and extends its concepts to infinite-dimensional settings, offering a unified approach to linear and nonlinear PDEs.
The book present a functional analytic perspective, focusing on well-posedness, solution theory, and operator-based techniques. Topics include abstract evolution equations, boundary value problems, integro-differential equations, delay systems, and applications in physics and engineering. The text emphasizes clarity, structure, and mathematical rigor, making it valuable for researchers and advanced graduate students.
The book also highlights how evolutionary equations can be applied to real-world models in continuum mechanics, thermodynamics, electromagnetism, and control theory. By combining theory with applications, the authors provide both conceptual depth and practical relevance.
Book Details & Specifications
Title:
Evolutionary Equations and Picard’s Theorem by Christian Seifert
Publisher:
Birkhäuser
Year:
2022
Pages:
619
Type:
PDF
Language:
English
ISBN-10 #:
3030893960
ISBN-13 #:
978-3030893965
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Christian Seifert
The author
Christian Seifert
is a mathematician with expertise in functional analysis and partial differential equations. His research focuses on solution theory for evolution equations and applications in mathematical physics. Sascha Trostorff works in operator theory and applied analysis. He studies PDEs in connection with physical models such as thermodynamics, elasticity, and control systems. Marcus Waurick specializes in evolution equations and homogenization theory. His work links abstract mathematics with applications in mechanics, electromagnetism, and materials science. Together, the authors bring a strong analytical background to the study of evolutionary equations and Picard's theorem for PDEs.
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