Degenerate Nonlinear Diffusion Equations
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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
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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.
Recent Results On Selfsimilar Solutions Of Degenerate Nonlinear Diffusion Equations
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Author : J. Hulshof
language : en
Publisher:
Release Date : 1994
Recent Results On Selfsimilar Solutions Of Degenerate Nonlinear Diffusion Equations written by J. Hulshof and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Evolution Equations Control Theory And Biomathematics
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Author : Philippe Clement
language : en
Publisher: CRC Press
Release Date : 1993-11-23
Evolution Equations Control Theory And Biomathematics written by Philippe Clement and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-23 with Mathematics categories.
Based on the Third International Workshop Conference on Evolution Equations, Control Theory and Biomathematics, held in Hans-sur-Lesse, Belgium. The papers examine important advances in evolution equations related to physical, engineering and biological applications.
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.
Travelling Waves In Nonlinear Diffusion Convection Reaction
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Author : Brian H. Gilding
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Travelling Waves In Nonlinear Diffusion Convection Reaction written by Brian H. Gilding and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 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.
Degenerate Nonlinear Diffusion Equations
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Author : Angelo Favini
language : en
Publisher: Springer
Release Date : 2012-05-09
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 2012-05-09 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.
Mathematical Ecology
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Author : S.A. Levin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-13
Mathematical Ecology written by S.A. Levin 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 2013-03-13 with Science categories.