  By a maximum principle under global control map from $R^{n+1}$ to$S^2,$
$\delta $-viscosity supersolution and subsolution of multidimensional
Landau-Lifshitz equations with second approximation of effective field are
built. Utilizing the $\delta $-viscosity supersolution and subsolution, the
viscosity solution of the equations is showed and the limiting behavior of the
solution of the equations is obtained. Exactly, there exist two disjoint open
subsets such that the solutions tend to the point $(0,1,0)$ on arbitrary
compact subsets in one of them and tend to the point $(0,-1,0)$ on arbitrary
compact subsets in the other of them, respectively.
