Evolutionary Equations: Picard's Theorem for Partial Differential Equations, and Applications

This open-access book offers a solution theory for time-dependent partial differential equations,using Hilbert space methods and complex analysis. It demonstrates the applicability of the approach through various examples and develops a quantitative theory for evolutionary equations, making it a valuable resource for beginners and a bridge to advanced research.

Format: Paperback / softback
Length: 317 pages
Publication date: 03 February 2022
Publisher: Springer Nature Switzerland AG

This open-access book presents a comprehensive solution theory for time-dependent partial differential equations, a domain that has historically been challenging to approach using a unified method. Instead of relying on sophisticated techniques and methodologies, the approach is remarkably elementary, requiring only Hilbert space methods and a fundamental understanding of complex analysis. Despite its simplicity, the method possesses remarkable capabilities, enabling the recovery of key properties of solutions in a graceful and elegant manner. Furthermore, the strength of this approach is substantiated through a diverse range of examples, showcasing its applicability across various fields. Additionally, a quantitative theory for evolutionary equations is developed, providing a deeper understanding of the underlying dynamics.

The book is self-contained, making it an ideal resource for individuals embarking on their first exploration of evolutionary equations. It also serves as a valuable guide to the extensive literature available on this subject, effectively bridging the gap between novice and advanced mathematical research. By offering a comprehensive and accessible approach, this book contributes to the advancement of knowledge in this field and paves the way for further developments in mathematical sciences.

Weight: 510g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030893996
Edition number: 1st ed. 2022