Affiliation:
1. Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, Japan
Abstract
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 theory relative to Mosco convergence and evolution equations governed by time-dependent subdifferentials is developed until the periodic problem falls within its scope. Further application of this approach to the limiting problem of porous-medium-type equations, such asut=Δ|u|m−2uasm→+∞, is also given.
Subject
Applied Mathematics,Analysis
Cited by
5 articles.
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