Description
Differential Equations on Measures and Functional Spaces, 1st ed. 2019
Birkhäuser Advanced Texts Basler Lehrbücher Series
Author: Kolokoltsov Vassili
Language: EnglishSubject for Differential Equations on Measures and Functional Spaces:
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
525 p. · 15.5x23.5 cm · Hardback
Description
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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.
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.
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