ASYMPTOTIC-BEHAVIOR OF THE SOLUTIONS OF NONLINEAR ELLIPTIC AND PARABOLIC-SYSTEMS IN TUBE DOMAINS

The paper is devoted to the study of the asymptotic behaviour of solut ions of weakly non-linear elliptic and parabolic systems of second-ord er equations. In particular, the behaviour as t --> + infinity of the solution of a second-order non-linear parabolic equation satisfying a Neumann boundary condition at the boundary of a bounded Lipschitz doma in is studied. The proofs are based-on a result on the asymptotic equi valence of two systems of ordinary differential equations.