Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T12:08:55.854Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay estimates in the supremum norm for the solutions to a nonlinear evolution equation

Published online by Cambridge University Press:  16 May 2014

Petri Juutinen
Petri Juutinen*
Affiliation:
Department of Mathematics and Statistics, PO Box 35, FIN-40014, University of Jyväskylä, Finland, ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the asymptotic behaviour, as t → ∞, of the solutions to the nonlinear evolution equation

where ΔpNu = Δu + (p−2) (D2u(Du/∣Du∣)) · (Du/∣Du∣) is the normalized p-Laplace equation and p ≥ 2. We show that if u(x,t) is a viscosity solution to the above equation in a cylinder Ω × (0, ∞) with time-independent lateral boundary values, then it converges to the unique stationary solution h as t → ∞. Moreover, we provide an estimate for the decay rate of maxx∈Ω∣u(x,t) − h(x)∣.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 3 , June 2014 , pp. 557 - 566
Copyright
Copyright © Royal Society of Edinburgh 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)