Nonautonomous Fractional Evolution Equations
Nonautonomous Fractional Evolution Equations

Author: Yong Zhou

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-07-01

Total Pages: 314

ISBN-13: 311139218X

DOWNLOAD EBOOK

Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.

Nonautonomous Fractional Evolution Equations
Nonautonomous Fractional Evolution Equations

Author: Yong Zhou

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2024-07-01

Total Pages: 258

ISBN-13: 3111391248

DOWNLOAD EBOOK

Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.

Stochastic Evolution Equations
Stochastic Evolution Equations

Author: Wilfried Grecksch

Publisher: De Gruyter Akademie Forschung

Published: 1995

Total Pages: 188

ISBN-13:

DOWNLOAD EBOOK

The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.

Evolution Equations
Evolution Equations

Author: Kaïs Ammari

Publisher: Cambridge University Press

Published: 2018

Total Pages: 205

ISBN-13: 1108412300

DOWNLOAD EBOOK

The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Evolution Equations
Evolution Equations

Author: Aleksandr Andreevich Pankov

Publisher:

Published: 2018

Total Pages: 340

ISBN-13: 9781536142594

DOWNLOAD EBOOK

This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.

The Analysis of Fractional Differential Equations
The Analysis of Fractional Differential Equations

Author: Kai Diethelm

Publisher: Springer

Published: 2010-08-18

Total Pages: 251

ISBN-13: 3642145744

DOWNLOAD EBOOK

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Nonautonomous Dynamical Systems
Nonautonomous Dynamical Systems

Author: Peter E. Kloeden

Publisher: American Mathematical Soc.

Published: 2011-08-17

Total Pages: 274

ISBN-13: 0821868713

DOWNLOAD EBOOK

The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness
Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

Author: Józef Banaś

Publisher: Springer

Published: 2017-05-04

Total Pages: 0

ISBN-13: 9789811037214

DOWNLOAD EBOOK

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.

Harmonic Analysis Method For Nonlinear Evolution Equations, I
Harmonic Analysis Method For Nonlinear Evolution Equations, I

Author: Baoxiang Wang

Publisher: World Scientific

Published: 2011-08-10

Total Pages: 298

ISBN-13: 9814458392

DOWNLOAD EBOOK

This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

Generalized Fractional Calculus and Applications
Generalized Fractional Calculus and Applications

Author: Virginia S Kiryakova

Publisher: CRC Press

Published: 1993-12-27

Total Pages: 412

ISBN-13: 9780582219779

DOWNLOAD EBOOK

In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.