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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
