Nonlinear Diffusion Problems

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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.

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.

Nonlinear Diffusion Problems

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Author : Michiel Bertsch
language : en
Publisher:
Release Date : 1983

Nonlinear Diffusion Problems written by Michiel Bertsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

Nonlinear Diffusion Problems

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Author : O. Diekmann
language : en
Publisher:
Release Date : 1976

Nonlinear Diffusion Problems written by O. Diekmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Differential equations, Nonlinear categories.

Nonlinear Diffusion Equations And Their Equilibrium States 3

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Author : N.G Lloyd
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-06-01

Nonlinear Diffusion Equations And Their Equilibrium States 3 written by N.G Lloyd 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 1991-06-01 with Mathematics categories.

Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Nonlinear Diffusion Problems

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Author : Cornelis J. van Duyn
language : en
Publisher:
Release Date : 1979

Nonlinear Diffusion Problems written by Cornelis J. van Duyn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.

Smoothing And Decay Estimates For Nonlinear Diffusion Equations

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Author : Juan Luis Vázquez
language : en
Publisher: OUP Oxford
Release Date : 2006-08-03

Smoothing And Decay Estimates For Nonlinear Diffusion Equations written by Juan Luis Vázquez and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-03 with Mathematics categories.

This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis. Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.

Degenerate Nonlinear Diffusion Equations

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Author : Angelo Favini
language : en
Publisher: Springer
Release Date : 2012-05-08

Degenerate Nonlinear Diffusion Equations written by Angelo Favini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-08 with Mathematics categories.

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.

Nonlinear Diffusion Equations And Their Equilibrium States I

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Author : W.-M. Ni
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Diffusion Equations And Their Equilibrium States I written by W.-M. Ni 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 2012-12-06 with Mathematics categories.

In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.

Nonlinear Diffusion Problems

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Author : Odo Diekmann
language : en
Publisher:
Release Date : 1976

Nonlinear Diffusion Problems written by Odo Diekmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.