MPEJ Volume 12, No. 5, 21 pp.
Received: Mai 13, 2005. Revised: Sep 11, 2006. Accepted:  Oct 16, 2006.

M.A. Rincon, J. Limaco, I-S. Liu
A Nonlinear Heat Equation with Temperature-Dependent Parameters

ABSTRACT: A nonlinear partial differential equation of the following form is
considered:
$$
 u'-\div\Big(a(u)\nabla u\Big)+ b(u)\;\vert\nabla u\vert^2=0,
$$
which arises from the heat conduction problems with strong
temperature-dependent material parameters, such as mass density, specific heat
and heat conductivity. Existence, uniqueness and asymptotic behavior of initial
boundary value problems under appropriate assumptions on the material
parameters are established for one-dimensional case. Existence and asymptotic
behavior for two-dimensional case are also proved.

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