Evolutionary Equations : Picard's Theorem for Partial Differential Equations, and Applications / by Christian Seifert, Sascha Trostorff, Marcus Waurick.

Format:

Book

Author/Creator:

Seifert, Christian.

Contributor:

Trostorff, Sascha, 1984-

Waurick, Marcus.

Series:

Operator Theory: Advances and Applications, 2296-4878 ; 287

Language:

English

Subjects (All):

Differential equations.

Differential Equations.

Local Subjects:

Differential Equations.

Physical Description:

1 online resource (321 pages)

Edition:

1st ed. 2022.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2022.

Language Note:

English

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.

Contents:

- 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.

ISBN:

3-030-89397-9

OCLC:

1299382308