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Differential Equations on Measures and Functional Spaces

  • Vassili Kolokoltsov
Textbook

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Vassili Kolokoltsov
    Pages 1-84
  3. Vassili Kolokoltsov
    Pages 85-158
  4. Vassili Kolokoltsov
    Pages 159-211
  5. Vassili Kolokoltsov
    Pages 213-287
  6. Vassili Kolokoltsov
    Pages 289-359
  7. Vassili Kolokoltsov
    Pages 361-404
  8. Vassili Kolokoltsov
    Pages 405-441
  9. Vassili Kolokoltsov
    Pages 443-480
  10. Vassili Kolokoltsov
    Pages 481-501
  11. Back Matter
    Pages 503-525

About this book

Introduction

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. 

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

Authors and affiliations

  • Vassili Kolokoltsov
    • 1
  1. 1.Department of Statistics, University of Warwick, Warwick, UKHigher School of EconomicsMoscowRussia

Bibliographic information