Abstract :
In this paper we investigate the existence, uniqueness, and asymptotic behavior
of a solution for a class of coupled nonlinear parabolic equations in a general
unbounded domain that includes the whole space Rn, the exterior of a bounded
domain, and a half space in Rn. The asymptotic behavior of the solution is with
respect to a pair of quasi-solutions of the corresponding elliptic system, and when
these two quasi-solutions coincide the solution of the parabolic system converges to
a unique solution of the elliptic system.
