| Contents |
| This paper is concerned with viscosity solutions for a class of degenerate
quasilinear parabolic equations in a bounded domain under nonlinear boundary
conditions. The equation under consideration arises from a number of
practical model problems, including heat-transfer problems, chemical
reactions, and reaction-diffusion processes in porous media. The goal of
this paper is: to prove the existence of a continuous viscosity solution and
its comparison property with viscosity upper and lower solutions, to
investigate the relationship between the viscosity solution and the
classical and weak solutions, and to investigate the asymptotic behavior of
the classical solution. Conditions are obtained to ensure that the viscosity
solution coincides or evolves into a unique classical solution which leads
to some dynamic property of the solution in relation to the positive
steady-state solutions. An application of these results is given to a heat
transfer problem where the thermal conductivity is temperature dependent and
the boundary condition follows a fourth-power radiation law. |
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