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Nonlinear Diffusion Equations and Their Equilibrium States II - Proceedings of a Microprogram held August 25-September 12, 1986 (Paperback, Softcover reprint of the original 1st ed. 1988)
Loot Price: R2,984
Discovery Miles 29 840
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Nonlinear Diffusion Equations and Their Equilibrium States II - Proceedings of a Microprogram held August 25-September 12, 1986 (Paperback, Softcover reprint of the original 1st ed. 1988)
Series: Mathematical Sciences Research Institute Publications, 13
Expected to ship within 10 - 15 working days
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Total price: R3,004
Discovery Miles: 30 040
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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.
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