Distributions in the Physical and Engineering Sciences: Volumes 1-3

ISBN-13: 9783030017927 / Angielski / Twarda / 2018

Alexander I. Saichev; Wojbor A. Woyczynski

Spis treści

Volume 1: Distributional and Fractal Calculus, Integral Transforms, and Wavelets.- Part I: Distributions and Their Basic Applications.- Basic Definitions and Operations.- Basic Applications: Rigorous and Pragmatic.- Part II: Integral Transforms and Divergent Series.- Fourier Transform.- Asymptotics of Fourier Transforms.- Stationary Phase and Related Method.- Singular Integrals and Fractal Calculus.- Uncertainty Principle and Wavelet Transforms.- Summation of Divergent Series and Integrals.- Answers and Solutions.- References.- Index.- Volume 2: Linear and Nonlinear Dynamics in Continuous Media.- Part III: Potentials, Diffusions, and Waves.- Potential Theory and Fundamental Solutions of Elliptic Equations.- Diffusions and Parabolic Evolution Equations.- Waves and Hyperbolic Equations.- Part IV: Nonlinear Partial Differential Equations.- First-Order Nonlinear PDEs and Conservation Laws.- Generalized Solutions of First-Order Nonlinear PDEs.- Nonlinear Waves and Growing Interfaces: 1-D Burgers-KPZ Models.- Other Standard Nonlinear Models of Higher Order.- Answers and Solutions.- References.- Index.- Volume 3: Random and Anomalous Fractional Dynamics in Continuous Media.- Part V: Random Dynamics.- Basic Distributional Tools for Probability Theory.- Random Distributions: Generalized Stochastic Processes.- Dynamical and Statistical Characteristics of Random Fields and Waves.- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows.- Probability Distributions of Passive Tracers in Randomly Moving Media.- Part VI: Anomalous Fractional Dynamics.- Levy Processes and their Generalized Derivatives.- Linear Anomalous Fractional Dynamics in Continuous Media.- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media.- Appendix: Basic Facts about Distributions.- References.- Index.

O autorze

Alexander I. Saichev was Professor of Mathematics at the Radio Physics Faculty of the Nizhny Novgorod University and a Professor in the Department of Management, Technology, and Economics at the Swiss Federal Institute of Technology.

Wojbor A. Woyczynski is Professor of Mathematics and Director of the Center for Stochastic and Chaotic Processes in Science and Technology at Case Western University.