Nonlinear Diffusion Equations

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Publisher : World Scientific
ISBN 13 : 9810247184
Total Pages : 521 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Nonlinear Diffusion Equations by : Zhuoqun Wu

Download or read book Nonlinear Diffusion Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2001 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Nonlinear Diffusion Equation

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Publisher : Springer Science & Business Media
ISBN 13 : 940101745X
Total Pages : 183 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis The Nonlinear Diffusion Equation by : J.M. Burgers

Download or read book The Nonlinear Diffusion Equation written by J.M. Burgers and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the 'Introduction' to the main text gives an account of the way in which the problems treated in the following pages originated, this 'Preface' may be limited to an acknowledgement of the support the work has received. It started during the pe riod when I was professor of aero- and hydrodynamics at the Technical University in Delft, Netherlands, and many discussions with colleagues ha ve in:fluenced its devel opment. Oftheir names I mention here only that ofH. A. Kramers. Papers No. 1-13 ofthe list given at the end ofthe text were written during that period. Severa! ofthese were attempts to explore ideas which later had to be abandoned, but gradually a line of thought emerged which promised more definite results. This line began to come to the foreground in pa per No. 3 (1939}, while a preliminary formulation ofthe results was given in paper No. 12 (1954}. At that time, however, there still was missing a practica! method for manipulating a certain distribution function of central interest. A six months stay at the Hydrodynamics Laboratories ofthe California Institute of Technology, Pasadena, California (1950-1951}, was supported by a Contract with the Department of the Air F orce, N o. AF 33(038}-17207. A course of lectures was given during this period, which were published in typescript under the title 'On Turbulent Fluid Motion', as Report No. E-34. 1, July 1951, of the Hydrodynamics Laboratory.

Degenerate Nonlinear Diffusion Equations

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Publisher : Springer
ISBN 13 : 3642282857
Total Pages : 165 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Degenerate Nonlinear Diffusion Equations by : Angelo Favini

Download or read book Degenerate Nonlinear Diffusion Equations written by Angelo Favini and published by Springer. This book was released on 2012-05-08 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce relevant solving methods for each of them.

Nonlocal Diffusion Problems

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Publisher : American Mathematical Soc.
ISBN 13 : 0821852302
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlocal Diffusion Problems by : Fuensanta Andreu-Vaillo

Download or read book Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo and published by American Mathematical Soc.. This book was released on 2010 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.

Nonlinear Diffusion Problems

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Publisher : Springer
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis Nonlinear Diffusion Problems by : Centro internazionale matematico estivo

Download or read book Nonlinear Diffusion Problems written by Centro internazionale matematico estivo and published by Springer. This book was released on 1986 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise

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Author :
Publisher : Springer
ISBN 13 : 3319008285
Total Pages : 175 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise by : Arnaud Debussche

Download or read book The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise written by Arnaud Debussche and published by Springer. This book was released on 2013-10-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

Nonlinear Reaction-Diffusion Systems

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Publisher : Springer
ISBN 13 : 3319654675
Total Pages : 173 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Nonlinear Reaction-Diffusion Systems by : Roman Cherniha

Download or read book Nonlinear Reaction-Diffusion Systems written by Roman Cherniha and published by Springer. This book was released on 2017-09-18 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.

A Closer Look of Nonlinear Reaction-Diffusion Equations

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Author :
Publisher : Nova Science Publishers
ISBN 13 : 9781536183566
Total Pages : 207 pages
Book Rating : 4.1/5 (835 download)

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Book Synopsis A Closer Look of Nonlinear Reaction-Diffusion Equations by : Lakshmanan Rajendran

Download or read book A Closer Look of Nonlinear Reaction-Diffusion Equations written by Lakshmanan Rajendran and published by Nova Science Publishers. This book was released on 2020-10 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Smoothing and Decay Estimates for Nonlinear Diffusion Equations

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Publisher : Oxford University Press, USA
ISBN 13 : 0199202974
Total Pages : 249 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Smoothing and Decay Estimates for Nonlinear Diffusion Equations by : Juan Luis Vázquez

Download or read book Smoothing and Decay Estimates for Nonlinear Diffusion Equations written by Juan Luis Vázquez and published by Oxford University Press, USA. This book was released on 2006-08-03 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, whichappear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.

Nonlinear Parabolic and Elliptic Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 1461530342
Total Pages : 786 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Nonlinear Parabolic and Elliptic Equations by : C.V. Pao

Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

Semigroup Approach To Nonlinear Diffusion Equations

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Publisher : World Scientific
ISBN 13 : 981124653X
Total Pages : 221 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Semigroup Approach To Nonlinear Diffusion Equations by : Viorel Barbu

Download or read book Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and published by World Scientific. This book was released on 2021-09-23 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Travelling Waves in Nonlinear Diffusion-Convection Reaction

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Publisher : Springer Science & Business Media
ISBN 13 : 9783764370718
Total Pages : 224 pages
Book Rating : 4.3/5 (77 download)

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Book Synopsis Travelling Waves in Nonlinear Diffusion-Convection Reaction by : Brian H. Gilding

Download or read book Travelling Waves in Nonlinear Diffusion-Convection Reaction written by Brian H. Gilding and published by Springer Science & Business Media. This book was released on 2004-07-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.

Nonlinear Diffusion of Electromagnetic Fields

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Publisher : Elsevier
ISBN 13 : 0080537693
Total Pages : 429 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Nonlinear Diffusion of Electromagnetic Fields by :

Download or read book Nonlinear Diffusion of Electromagnetic Fields written by and published by Elsevier. This book was released on 1998-04-28 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)

The Porous Medium Equation

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Publisher : Clarendon Press
ISBN 13 : 0191513830
Total Pages : 648 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis The Porous Medium Equation by : Juan Luis Vazquez

Download or read book The Porous Medium Equation written by Juan Luis Vazquez and published by Clarendon Press. This book was released on 2006-10-26 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, and other fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.

An Introduction to Nonlinear Partial Differential Equations

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Publisher : John Wiley & Sons
ISBN 13 : 0470225955
Total Pages : 416 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis An Introduction to Nonlinear Partial Differential Equations by : J. David Logan

Download or read book An Introduction to Nonlinear Partial Differential Equations written by J. David Logan and published by John Wiley & Sons. This book was released on 2008-04-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79

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Publisher : World Scientific
ISBN 13 : 9789810241476
Total Pages : 576 pages
Book Rating : 4.2/5 (414 download)

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Book Synopsis Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79 by : M. Boiti

Download or read book Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79 written by M. Boiti and published by World Scientific. This book was released on 2000 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems ? classical and quantum ? are considered.

Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions

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Publisher : Springer
ISBN 13 : 3319614940
Total Pages : 288 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions by : José Antonio Carrillo

Download or read book Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions written by José Antonio Carrillo and published by Springer. This book was released on 2017-10-03 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems. The authors are some of the most well-known mathematicians in this innovative field, which is presently undergoing rapid development. The intended audience includes experts in elliptic and parabolic equations who are interested in extending their expertise to the nonlinear setting, as well as Ph.D. or postdoctoral students who want to enter into the most promising research topics in the field.