Beyond PDEs: Hyperbolic Evolution Equations by Horst R. Beyer
Beyond PDEs: Hyperbolic Evolution Equations - Table of Contents
1. General Introduction
2. Conventions
3. Mathematical Introduction
4. Prerequisites
5. Strongly Continuous Semigroups
6. Examples of Generators of Strongly Continuous Semigroups
7. Intertwining Relations, Operator Homomorphisms
8. Examples of Constrained Systems
9. Kernels, chains, and Evolution Operators
10. The Linear Evolution Equation
11. Examples of Linear Evolution Equations
12. The Quasi-Linear Evolution Equation
13. Examples of Quasi-Linear Evolution Equations
What You Will Learn in Beyond PDEs: Hyperbolic Evolution Equations
"Beyond Partial Differential Equations: A course on Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations" by Horst R. Beyer is an advanced and rigorous text exploring the mathematical foundations of "hyperbolic evolution equations". It extends the study of traditional "partial differential equations" to a broader framework, showing how complex systems evolve over time in both classical and modern applications. The book is designed for graduate students and researchers with a strong background in "functional analysis", operator theory, and applied mathematics.
The text introduces methods from "semigroup theory" to handle both "linear" and quasi-linear evolution problems. It demonstrates how strongly continuous semigroups on Hilbert and Banach spaces can be used to describe the dynamics of systems, including wave propagation, quantum mechanics, and relativistic models. Beyer emphasizes the unified treatment of evolution equations beyond standard PDE techniques, highlighting connections between abstract theory and physically relevant applications. The book includes examples of constrained systems and wave equations, illustrating how abstract methods lead to concrete solutions.
One of the key strengths of this book is its ability to bridge classical PDE theory with modern operator-based approaches. By combining "analysis", "hyperbolic equations", and semigroup techniques, it provides readers with a deep understanding of the mathematical structures governing time-dependent systems. Overall, "Beyond PDEs" is an essential resource for those seeking expertise in advanced applied mathematics, mathematical physics, and the theory of evolution equations.
Book Details & Specifications
Title:
Beyond PDEs: Hyperbolic Evolution Equations by Horst R. Beyer
Publisher:
Arxiv
Year:
2011
Pages:
275
Type:
PDF
Language:
English
ISBN-10 #:
3540711287
ISBN-13 #:
978-3540711285
License:
Arxiv License
Amazon:
Amazon
About the Author: Horst R. Beyer
The author
Horst R. Beyer
is a mathematician known for his work in "Partial Differential Equations" and "Hyperbolic Evolution Equations". While details about his birthplace and early education are limited, he holds a doctoral degree and has served in research and teaching positions at institutions including "Louisiana State University". His expertise spans "Functional Analysis", "Semigroup Methods", and "Mathematical Physics". In "Beyond PDEs: Hyperbolic Evolution Equations", Beyer explores advanced analytic techniques, connecting abstract theory with applications in physics and differential systems, providing students and researchers with a rigorous and practical approach to complex mathematical problems.
Read or Downloadable Beyond PDEs: Hyperbolic Evolution Equations
Free Differential Equations Books PDF | Curated Academic Index