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Title
Evolutionary equations : Picard's theorem for partial differential equations, and applications / Christian Seifert, Sascha Trostorff, Marcus Waurick.
ISBN
9783030893972 (electronic bk.)
3030893979 (electronic bk.)
9783030893965
Published
Cham : Birkhäuser, [2022]
Copyright
©2022
Language
English
Description
1 online resource (xii, 317 pages) : illustrations.
Item Number
10.1007/978-3-030-89397-2 doi
Call Number
QA377.3 .S45 2022
Dewey Decimal Classification
515/.353
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Open access
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 11, 2022).
Series
Operator theory, advances and applications ; v. 287. 2296-4878
- Introduction
Unbounded Operators
The Time Derivative
Ordinary Differential Equations
The Fourier-Laplace Transformation and Material Law Operators
Solution Theory for Evolutionary Equations
Examples of Evolutionary Equations
Causality and a Theorem of Paley and Wiener
Initial Value Problems and Extrapolation Spaces
Differential Algebraic Equations
Exponential Stability of Evolutionary Equations
Boundary Value Problems and Boundary Value Spaces
Continuous Dependence on the Coefficients I
Continuous Dependence on the Coefficients II.
