Differential Equations on Measures and Functional Spaces
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Beschreibung
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, mutations and 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.
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.
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
Autor*in
Vassili Kolokoltsov
Themen in »Differential Equations on Measures and Functional Spaces«
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
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“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)
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