Abstract
The paper is devoted to the study of the asymptotic behaviour of solutions of weakly non-linear elliptic and parabolic systems of second-order equations. In particular, the behaviour as of the solution of a second-order non-linear parabolic equation satisfying a Neumann boundary condition at the boundary of a bounded Lipschitz domain is studied. The proofs are based on a result on the asymptotic equivalence of two systems of ordinary differential equations.
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