Overview
- This book presents a joint discussion of theoretical tools and recent applications in PDE theory
- The matierial offers both state of the art and latest developments with updated and comparative literature
- The presentation is for specialists and it is also kept fully accessible by a junior graduate readership
Part of the book series: Springer INdAM Series (SINDAMS, volume 52)
Included in the following conference series:
Conference proceedings info: INdAM 2021.
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About this book
This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.
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Keywords
Table of contents (10 papers)
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Front Matter
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Long-Time Behavior of NLS-Type Equations
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Front Matter
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Probabilistic and Nonstandard Methods in the Study of NLS Equations
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Front Matter
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Back Matter
Other volumes
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Qualitative Properties of Dispersive PDEs
Editors and Affiliations
About the editors
Vladimir Georgiev is a former Alexander von Humboldt fellow. He is a Full Professor of mathematics at the University of Pisa. The main fields of the research interests involve decay estimates for equations of Mathematical Physics on flat or curved space - time, smoothing and Strichartz estimates for evolution problems, global existence of small and large data solutions to equations of classical quantum mechanics, existence and stability of solitary waves, Maxwell–Dirac and Maxwell–Scrödinger equation, scattering and long range effects for relativistic and non – relativistic particles and fields.
Alessandro Michelangeli is an Alexander von Humboldt Senior Researcher at the Institute for Applied Mathematics and at the Hausdorff Center for Mathematics, Bonn, and a member of the Institute of Theoretical Quantum Technologies Trieste. He also held positions at the LMU Munich and the SISSA Trieste. His research is at the interface of analysis, mathematical physics,and theoretical physics, with expertise in functional analysis, operator theory, spectral theory, non-linear partial differential equations, and quantum mechanics.
Raffaele Scandone is a postdoctoral researcher at Gran Sasso Science Institute, Italy. He received his PhD in Mathematics at SISSA, Italy, in 2014. His research interests lie in the area of dispersive PDEs, with a particular focus on Schrodinger-type equations and quantum hydrodynamics.
Bibliographic Information
Book Title: Qualitative Properties of Dispersive PDEs
Editors: Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone
Series Title: Springer INdAM Series
DOI: https://doi.org/10.1007/978-981-19-6434-3
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022
Hardcover ISBN: 978-981-19-6433-6Published: 03 December 2022
Softcover ISBN: 978-981-19-6436-7Published: 03 December 2023
eBook ISBN: 978-981-19-6434-3Published: 02 December 2022
Series ISSN: 2281-518X
Series E-ISSN: 2281-5198
Edition Number: 1
Number of Pages: XI, 245
Number of Illustrations: 1 b/w illustrations
Topics: Analysis, Functional Analysis