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Asymptotic behavior of solutions of some parabolic equation associated with thep-Laplacian asp→+∞is studied for the periodic problem as well as the initial-boundary value problem by pointing out the variational structure of thep-Laplacian, that is,∂φp(u)=−Δpu, whereφp:L2(Ω)→[0,+∞]. To this end, the notion of Mosco convergence is employed and it is proved thatφpconverges to the indicator function over some closed convex set onL2(Ω)in the sense of Mosco asp→+∞; moreover, an abstract theorydoi:10.1155/s1085337504403030 fatcat:hwbzq4kuircwdnw7zjhgkobkuu