Evolutionary Equations
Picard's Theorem for Partial Differential Equations, and Applications
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Beschreibung
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.
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.
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
Autor*in
Christian Seifert
Themen in »Evolutionary Equations«
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
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“The exposition is well written and clear, and many examples elucidate the theory. The text can be used as a textbook for teaching an advanced course on evolutionary PDEs and it is also suitable for self studying the topic.” (Kai Diethelm, zbMATH 1497.35008, 2022)
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