Abstract and Applied Analysis
Volume 2004 (2004), Issue 11, Pages 907-933
Convergence of functionals and its applications to parabolic equations
Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, Japan
Received 11 December 2003
Copyright © 2004 Goro Akagi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Asymptotic behavior of solutions of some parabolic equation associated with the -Laplacian as is studied for the periodic problem as well as the initial-boundary value problem by pointing out the variational structure of the -Laplacian, that is, , where . To this end, the notion of Mosco convergence is employed and it is proved that converges to the indicator function over some closed convex set on in the sense of Mosco as ; 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 as as , is also given.