The Correspondence Between Travelling-wave Solutions of a Nonlinear Reaction-convection-diffusion Equation and an Integral Equation PDF Download
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Author: B. H. Gilding
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Author: B. H. Gilding
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
Author: Brian H. Gilding
Publisher: Birkhäuser
ISBN: 3034879644
Category : Mathematics
Languages : en
Pages : 214
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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.
Author:
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ISBN:
Category : Differential equations
Languages : en
Pages : 332
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Author: Victor A. Galaktionov
Publisher: CRC Press
ISBN: 0203998065
Category : Mathematics
Languages : en
Pages : 384
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Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Plya in the 1930's and rediscovered in part several times since, it was not un
Author: Hinwa Leung
Publisher:
ISBN:
Category : Differential equations, Nonlinear
Languages : en
Pages : 176
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ISBN:
Category : Aeronautics
Languages : en
Pages : 772
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Author:
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 668
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Author: P. Knabner
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: W.-M. Ni
Publisher: Springer Science & Business Media
ISBN: 1461396085
Category : Mathematics
Languages : en
Pages : 364
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Book Description
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ 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 ~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.
