Convergence of functionals and its applications to parabolic equations

Goro Akagi

Abstract and Applied Analysis, 2004, vol. 2004, issue 11, 907-933

Abstract: Asymptotic behavior of solutions of some parabolic equation associated with the p‐Laplacian as p → +∞ is studied for the periodic problem as well as the initial‐boundary value problem by pointing out the variational structure of the p‐Laplacian, that is, ∂φp(u) = −Δpu, where φp : L2(Ω) → [0, +∞]. To this end, the notion of Mosco convergence is employed and it is proved that φp converges to the indicator function over some closed convex set on L2(Ω) in the sense of Mosco as p → +∞; 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 ut = Δ|u|m−2u as m → +∞, is also given.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/S1085337504403030

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2004:y:2004:i:11:p:907-933

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().