Convergence of functionals and its applications to parabolic equations

Goro Akagi
2004 Abstract and Applied Analysis  
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
more » ... tract 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.
doi:10.1155/s1085337504403030 fatcat:hwbzq4kuircwdnw7zjhgkobkuu