Abstract:

The purpose of this paper is to investigate the stability and asymptotic behavior
of the time-dependent solutions to a linear parabolic equation with nonlinear boundary
condition in relation to their corresponding steady state solutions. Then, the above results
are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing
the corresponding eigenvalue problem and using the method of upper and lower
solutions.

Key words: Asymptotic behavior;heat equation;nonlinear boundary condition, upper
and lower solutions