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Kolokoltsov, Vassili.

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Differential equations on measures and functional spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differential equations on measures and functional spaces/ by Vassili Kolokoltsov.
Author:	Kolokoltsov, Vassili.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xvi, 525 p. :ill., digital ;24 cm.
[NT 15003449]:	Analysis on measures and functional spaces -- Basic ODEs in complete locally convex spaces -- Discrete kinetic systems -- Linear evolutionary equations: foundations -- Linear evolutionary equations: advanced theory -- Method of propagators for nonlinear equations -- Equations in the spaces of weighted measures -- Generalized fractional differential equations -- Appendix.
Contained By:	Springer eBooks
Subject:	Differential equations. -
Online resource:	https://doi.org/10.1007/978-3-030-03377-4
ISBN:	9783030033774

Differential equations on measures and functional spaces
Kolokoltsov, Vassili.

Differential equations on measures and functional spaces[electronic resource] /by Vassili Kolokoltsov. - Cham :Springer International Publishing :2019. - xvi, 525 p. :ill., digital ;24 cm. - Birkhauser advanced texts basler lehrbucher,1019-6242. - Birkhauser advanced texts basler lehrbucher..

Analysis on measures and functional spaces -- Basic ODEs in complete locally convex spaces -- Discrete kinetic systems -- Linear evolutionary equations: foundations -- Linear evolutionary equations: advanced theory -- Method of propagators for nonlinear equations -- Equations in the spaces of weighted measures -- Generalized fractional differential equations -- Appendix.

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.

ISBN: 9783030033774

Standard No.: 10.1007/978-3-030-03377-4doiSubjects--Topical Terms:

517952
Differential equations.

LC Class. No.: QA371 / .K65 2019

Dewey Class. No.: 515.352

Differential equations on measures and functional spaces
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300 $a xvi, 525 p. : $b ill., digital ; $c 24 cm.
490 1 $a Birkhauser advanced texts basler lehrbucher, $x 1019-6242
505 0 $a Analysis on measures and functional spaces -- Basic ODEs in complete locally convex spaces -- Discrete kinetic systems -- Linear evolutionary equations: foundations -- Linear evolutionary equations: advanced theory -- Method of propagators for nonlinear equations -- Equations in the spaces of weighted measures -- Generalized fractional differential equations -- Appendix.
520 $a 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.
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