Differential Equations on Measures and Functional Spaces

1. Auflage 2019
ISBN: 978-3-030-03376-7
Verlag: Springer International Publishing

Buch, Englisch, 525 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 975 g

Reihe: Birkhäuser Advanced Texts Basler Lehrbücher

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Kolokoltsov, Vassili

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis

Inhaltsverzeichnis

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.

Über Autor(innen)

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.