Overview
- Combines uniquely deep abstract theory and the analysis of concrete equations
- Offers links to probability, control theory, game theory and interacting particles
- Exposes systematically the topic from its beginnings up to modern research results
- Introduces a new methodology of fast and unifying analysis of various equations inspired by modern developments in fractional calculus and in the theory of semigroups
- Includes previously unpublished material
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
- banach spaces
- locally convex spaces
- pseudo-differential operators and equations
- fractional differential equations
- Hamilton-Jacobi-Bellman equations
- forward-backward systems
- Schroedinger equation
- fractional Laplacian
- Boltzmann equation
- Smoluchovski equation
- Landau equation
- ODEs
- PDEs
- ordinary differential equations
- partial differential equations
About this book
This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutationsand the preferential-attachment growth on networks.
The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.
Reviews
“This book should be of high interest to people who do research in differential equations or their applications in stochastic processes, optimization, mathematical physics, interacting particle systems, and chemistry. This book is a genuine asset to a researcher in these or related areas; it presents a broad view of the presented mathematical results.” (J. A. van Casteren, Mathematical Reviews, June, 2020)
Authors and Affiliations
About the author
Vassili Kolokoltsov is a Professor at the University of Warwick with more than 100 papers and several monographs published. His general research interests are probability and stochastic processes, optimization and games with applications to business, biology and finances, mathematical physics, differential equations and functional analysis.
Bibliographic Information
Book Title: Differential Equations on Measures and Functional Spaces
Authors: Vassili Kolokoltsov
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-3-030-03377-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-03376-7Published: 01 July 2019
eBook ISBN: 978-3-030-03377-4Published: 20 June 2019
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: XVI, 525
Topics: Ordinary Differential Equations, Partial Differential Equations, Operator Theory, Game Theory, Economics, Social and Behav. Sciences