Degenerate Nonlinear Diffusion Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Degenerate Nonlinear Diffusion Equations write by Angelo Favini. This book was released on 2012-05-08. Degenerate Nonlinear Diffusion Equations available in PDF, EPUB and Kindle. 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
Nonlinear Diffusion Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Diffusion Equations write by Zhuoqun Wu. This book was released on 2001. Nonlinear Diffusion Equations available in PDF, EPUB and Kindle. 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
Recent Results on Selfsimilar Solutions of Degenerate Nonlinear Diffusion Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recent Results on Selfsimilar Solutions of Degenerate Nonlinear Diffusion Equations write by J. Hulshof. This book was released on 1994. Recent Results on Selfsimilar Solutions of Degenerate Nonlinear Diffusion Equations available in PDF, EPUB and Kindle.
Nonlinear Diffusion Equations and Their Equilibrium States I
Nonlinear Diffusion Equations and Their Equilibrium States I - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Diffusion Equations and Their Equilibrium States I write by W.-M. Ni. This book was released on 2012-12-06. Nonlinear Diffusion Equations and Their Equilibrium States I available in PDF, EPUB and Kindle. 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.
Travelling Waves in Nonlinear Diffusion-Convection Reaction
Travelling Waves in Nonlinear Diffusion-Convection Reaction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Travelling Waves in Nonlinear Diffusion-Convection Reaction write by Brian H. Gilding. This book was released on 2012-12-06. Travelling Waves in Nonlinear Diffusion-Convection Reaction available in PDF, EPUB and Kindle. 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.
