Nonlinear Diffusion

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Nonlinear Diffusion Equations

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Author : Zhuoqun Wu
language : en
Publisher: World Scientific
Release Date : 2001

Nonlinear Diffusion Equations written by Zhuoqun Wu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.

Nonlinear Diffusion Of Electromagnetic Fields

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Author :
language : en
Publisher: Elsevier
Release Date : 1998-04-28

Nonlinear Diffusion Of Electromagnetic Fields written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-28 with Science categories.

Nonlinear Diffusion of Electromagnetic Fields covers applications of the phenomena of non-linear diffusion of electromagnetic fields, such as magnetic recording, electromagnetic shielding and non-destructive testing, development of CAD software, and the design of magnetic components in electrical machinery. The material presented has direct applications to the analysis of eddy currents in magnetically nonlinear and hysteretic conductors and to the study of magnetization processes in electrically nonlinear superconductors. This book will provide very valuable technical and scientific information to a broad audience of engineers and researchers who are involved in these diverse areas. - Contains extensive use of analytical techniques for the solution of nonlinear problems of electromagnetic field diffusion - Simple analytical formulas for surface impedances of nonlinear and hysteretic media - Analysis of nonlinear diffusion for linear, circular and elliptical polarizations of electromagnetic fields - Novel and extensive analysis of eddy current losses in steel laminations for unidirectional and rotating magnetic fields - Preisach approach to the modeling of eddy current hysteresis and superconducting hysteresis - Extensive study of nonlinear diffusion in superconductors with gradual resistive transitions (scalar and vertorial problems)

Nonlinear Diffusion Equations

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Author : Huilai Li
language : en
Publisher: World Scientific
Release Date : 2001-11-12

Nonlinear Diffusion Equations written by Huilai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-12 with Mathematics categories.

Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.

Nonlinear Cosmic Ray Diffusion Theories

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Author : Andreas Shalchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-04

Nonlinear Cosmic Ray Diffusion Theories written by Andreas Shalchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-04 with Science categories.

If charged particles move through the interplanetary or interstellar medium, they interact with a large-scale magnetic ?eld such as the magnetic ?eld of the Sun or the Galactic magnetic ?eld. As these background ?elds are usually nearly constant in time and space, they can be approximated by a homogeneous ?eld. If there are no additional ?elds, the particle trajectory is a perfect helix along which the par- cle moves at a constant speed. In reality, however, there are turbulent electric and magnetic?elds dueto the interstellaror solar wind plasma. These ?elds lead to sc- tering of the cosmic rays parallel and perpendicular to the background ?eld. These scattering effects, which usually are of diffusive nature, can be described by s- tial diffusion coef?cients or, alternatively, by mean free paths. The knowledge of these parameters is essential for describing cosmic ray propagation as well as d- fusive shock acceleration. The latter process is responsible for the high cosmic ray energies that have been observed. The layout of this book is as follows. In Chap. 1, the general physical scenario is presented. We discuss fundamental processes such as cosmic ray propagation and acceleration in different systems such as the solar system or the interst- lar space. These processes are a consequence of the interaction between charged cosmic particles and an astrophysical plasma (turbulence). The properties of such plasmas are therefore the subject of Chap. 2.

Nonlinear Partial Differential Equations For Scientists And Engineers

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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

Nonlinear Partial Differential Equations For Scientists And Engineers written by Lokenath Debnath and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

"The book gives thorough coverage of the derivation and solution methods for all fundamental nonlinear model equations, such as Korteweg-de Vries, Camassa-Holm, Degasperis-Procesi, Euler-Poincare, Toda lattice, Boussinesq, Burgers, Fisher, Whitham, nonlinear Klein-Gordon, sine-Gordon, nonlinear Schrodinger, nonlinear reaction-diffustion, and Euler-Lagrange equations."--Page 4 of cover.

Nonlinear Signal And Image Processing

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Author : Kenneth E. Barner
language : en
Publisher: CRC Press
Release Date : 2003-11-24

Nonlinear Signal And Image Processing written by Kenneth E. Barner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-24 with Technology & Engineering categories.

Nonlinear signal and image processing methods are fast emerging as an alternative to established linear methods for meeting the challenges of increasingly sophisticated applications. Advances in computing performance and nonlinear theory are making nonlinear techniques not only viable, but practical. This book details recent advances in nonl

A Closer Look Of Nonlinear Reaction Diffusion Equations

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Author : L. Rajendran
language : en
Publisher: Nova Science Publishers
Release Date : 2020-08-26

A Closer Look Of Nonlinear Reaction Diffusion Equations written by L. Rajendran and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Reaction-diffusion equations categories.

By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area.Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science.This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples.Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations.Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.

Semigroup Approach To Nonlinear Diffusion Equations

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Author : Viorel Barbu
language : en
Publisher: World Scientific
Release Date : 2021-09-23

Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.

This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.

Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models

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Author : Roman M. Cherniha
language : en
Publisher: MDPI
Release Date : 2018-07-06

Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models written by Roman M. Cherniha and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.

This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry

The Nonlinear Diffusion Equation

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Author : Johannes Martinus Burgers
language : en
Publisher:
Release Date : 1974

The Nonlinear Diffusion Equation written by Johannes Martinus Burgers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.