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Nonlinear Diffusion Equations and Their Equilibrium States I Volume 12 by Ni, W.-M.; Peletier, L. A.; Serrin, James is a scholarly article available to read on EtoBox.

What is Nonlinear Diffusion Equations and Their Equilibrium States I Volume 12 about?

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

Author

Ni, W.-M.; Peletier, L. A.; Serrin, James

Publisher

Springer New York

Published

1988

Language

EN

ISBN

9781461396055